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NEET 2024
MCQ
At any instant of time t, the displacement of any particle is given by 2t-1 (SI unit) under the influence of force of 5N. The value of instantaneous power is (in SI unit)
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NEET 2024
MCQ
Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity $v_{1}$ while body B is at rest before collision. The velocity of the system after collision is $v_{2}$ . The ratio $v_{1}:v_{2}$ is
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JEE (Main) 2023
MCQ
As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball Q after collision will be $(g=10m/s^{2})$
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JEE (Main) 2023
MCQ
Identify the correct statements from the following
(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
(C) Work done by friction on a body sliding down an inclined plane is positive.
(D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.
(E) Work done by the air resistance on an oscillating pendulum is negative.
Choose the correct answer from the options given below
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NEET 2023
MCQ
The potential energy of a long spring when stretched by 2cm is U. If the spring is stretched by 8cm, potential energy stored in it will be
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JEE (Main) 2022
MCQ
A particle experiences a variable force $\vec{F} = (4x\hat{i} + 3y^2\hat{j})$ in a horizontal $x - y$ plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the $x - y$ plane, the kinetic energy changes by
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JEE (Main) 2022
MCQ
Potential energy as a function of r is given by $U = \frac{A}{r^{10}} - \frac{B}{r^{5}}$ , where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be
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JEE (Main) 2022
MCQ
A particle of mass 500 gm is moving in a straight line with velocity $v = bx^{5/2}$ . The work done by the net force during its displacement from x = 0 to x = 4m is (Take $b = 0.25 m^{-3/2} s^{-1}$ )
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JEE (Main) 2022
MCQ
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as $a = k^{2}rt^{2}$ . Where k is a constant. The power delivered to the particle by the force acting on it is given as
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JEE (Main) 2022
MCQ
A body of mass 0.5 kg travels on straight line path with velocity $v = (3x^{2} + 4)m/s$ . The net workdone by the force during its displacement from x = 0 to x = 2m is
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JEE (Main) 2022
MCQ
A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed $10 \, ms^{-1}$ gets embedded in it, then loss of kinetic energy will be
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JEE (Main) 2022
MCQ
A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be
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JEE (Main) 2022
MCQ
If momentum of a body is increased by 20%, then its kinetic energy increases by
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JEE (Main) 2022
MCQ
Sand is being dropped from a stationary dropper at a rate of $0.5 \, kgs^{-1}$ on a conveyor belt moving with a velocity of $5 \, ms^{-1}$ . The power needed to keep belt moving with the same velocity will be
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NEET 2022
MCQ
The energy that will be ideally radiated by a 100 kW transmitter in 1 hour is
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NEET 2022
MCQ
An electric lift with a maximum load of 2000 kg (lift+passengers) is moving up with a constant speed of $1.5 \, ms^{-1}$ . The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is $(g = 10 \, ms^{-2})$
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JEE (Main) 2021
MCQ
An object of mass $m_{1}$ collides with another object of mass $m_{2}$ , which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $m_{2}:m_{1}$ is
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JEE (Main) 2021
MCQ
A large block of wood of mass $M = 5.99 \, \text{kg}$ is hanging from two long massless cords. A bullet of mass $m = 10 \, \text{g}$ is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance $h = 9.8 \, \text{cm}$ before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is (Take $g = 9.8 \, \text{ms}^{-2}$ )
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JEE (Main) 2021
MCQ
A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of $20 \, ms^{-1}$ . The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now
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JEE (Main) 2021
MCQ
A porter lifts a heavy suitcase of mass $80\mathrm{kg}$ and at the destination lowers it down by a distance of $80~cm$ with a constant velocity. Calculate the workdone by the porter in lowering the suitcase (take $g = 9.8ms^{-2}$ )
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JEE (Main) 2021
MCQ
Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2 m and 2 m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is
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JEE (Main) 2021
MCQ
An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by
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JEE (Main) 2021
MCQ
A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of $0.8\sqrt{gh}$ . The value of work done by the air – friction is
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JEE (Main) 2021
MCQ
A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1:2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is
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JEE (Main) 2020
MCQ
A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to $(1\ \text{HP} = 746\ \text{W}, g = 10\ \text{ms}^{-2})$
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JEE (Main) 2020
MCQ
An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being $68\mathrm{kg}$ . The mass of the elevator itself is $920\mathrm{kg}$ and it moves with a constant speed $3\mathrm{m / s}$ . The frictional force opposing the motion is $6000N$ . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator $(g = 10m / s^2)$ must be at least
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JEE (Main) 2020
MCQ
A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$ . If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $\sqrt{\frac{h}{g}}$ is
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JEE (Main) 2020
MCQ
Consider a force $\vec{F} = -x\hat{i} + y\hat{j}$ . The work done by this force in moving a particle from point $A(1,0)$ to $B(0,1)$ along the line segment is (all quantities are in SI units)
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JEE (Main) 2020
MCQ
A particle of mass m is projected with a speed u from the ground at an angle $\theta=\frac{\pi}{3}w.r.t.$ horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $u\hat{i}$ . The horizontal distance covered by the combined mass before reaching the ground is
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JEE (Main) 2020
MCQ
A particle of mass m with an initial velocity $u\hat{i}$ collides perfectly elastically with a mass 3m at rest. It moves with a velocity $v\hat{j}$ after collision, then v is given by
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JEE (Main) 2020
MCQ
A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale)
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JEE (Main) 2020
MCQ
A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take $g=10m/s^{2}$ . Assume there is no rotational motion and loss of energy after the collision is negligible]
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JEE (Main) 2020
MCQ
Blocks of masses m, 2m, 4m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of 'p' is close to
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JEE (Main) 2020
MCQ
A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a distance of 15m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box
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JEE (Main) 2020
MCQ
Particle A of mass $m_{1}$ moving with velocity $(\sqrt{3}\hat{i}+\hat{j})ms^{-1}$ collides with another particle B of mass $m_{2}$ which is at rest initially. Let $\vec{v}_{1}$ and $\vec{v}_{2}$ be the velocities of particles A and B after collision respectively. If $m_{1}=2m_{2}$ and after collision $\vec{v}_{1}=(\hat{i}+\sqrt{3}\hat{j})ms^{-1}$ , the angle between $\vec{v}_{1}$ and $\vec{v}_{2}$ is
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JEE (Main) 2019
MCQ
A force acts on a 2kg object so that its position is given as a function of time as $x = 3t^{2} + 5$ . What is the work done by this force in first 5 seconds
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JEE (Main) 2019
MCQ
Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an brutal speed v towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically $\frac{5}{6}th$ of the initial kinetic energy is lost in whole process. What is value of M/m
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JEE (Main) 2019
MCQ
A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg if fired vertically upward, with a velocity $100 \, ms^{-1}$ , from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is $(g = 10 \, \text{ms}^{-2})$
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JEE (Main) 2019
MCQ
A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in fig. Work done by normal reaction on block in time t is
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JEE (Main) 2019
MCQ
A particle which is experiencing a force, given by $\vec{F} = 3\vec{i} - 12\vec{j}$ , undergoes a displacement of $\vec{d} = 4\vec{i}$ . If the particle had a kinetic energy of $3J$ at the beginning of the displacement, what is its kinetic energy at the end of the displacement
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JEE (Main) 2019
MCQ
A body of mass 1 kg falls freely from a height of 100 m on a platform of mass 3 kg which is mounted on a spring having spring constant $k = 1.25 \times 10^{6} N/m$ . The body sticks to the platform and the spring's maximum compression is found to be x. Given that $g = 10 ms^{-2}$ , the value of x will be close to
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JEE (Main) 2019
MCQ
An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus
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JEE (Main) 2019
MCQ
A particle moves in the one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3m is
(in $m$ )
Errorless
JEE (Main) 2019
MCQ
A body of mass $m_{1}$ moving with an unknown velocity of $v_{1}\hat{i}$ , undergoes a collinear collision with a body of mass $m_{2}$ moving with a velocity $v_{2}\hat{i}$ . After collision, $m_{1}$ and $m_{2}$ move with velocities of $v_{3}\hat{i}$ and $v_{4}\hat{i}$ , respectively. If $m_{2}=0.5m_{1}$ and $v_{3}=0.5v_{1}$ , then $v_{1}$ is
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JEE (Main) 2019
MCQ
A uniform cable of mass ‘M’ and length ‘L’ is placed on a horizontal surface such that its $\left(\frac{1}{n}\right)^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable up to the surface, the work done should be
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JEE (Main) 2019
MCQ
A particle of mass ‘m’ is moving with speed ‘2v’ and collides with a mass ‘2m’ moving with speed ‘v’ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass ‘m’, which move at angle $45^{\circ}$ with respect to the original direction. The speed of each of the moving particle will be
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JEE (Main) 2019
MCQ
A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by
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JEE (Main) 2019
MCQ
Two particles, of masses $M$ and $2M$ , moving, as shown, with speeds of $10~m / s$ and $5m / s$ , collide elastically at the origin. After the collision, they move along the indicated directions with speeds $v_{1}$ and $v_{2}$ , respectively. The values of $v_{1}$ and $v_{2}$ are nearly
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JEE (Main) 2019
MCQ
A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body
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NEET 2019
MCQ
Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is
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NEET 2019
MCQ
A force $F = 20 + 10y$ acts on a particle in $y$ -direction where $F$ is in newton and $y$ in meter. Work done by this force to move the particle from $y = 0$ to $y = 1m$ is
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NEET 2018
MCQ
A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to
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JEE (Main) 2018
MCQ
A particle is moving in a circular path of radius a under the action of an attractive potential $U = \frac{k}{2r^{2}}$ . Its total energy is
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NEET 2018
MCQ
A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of resistitution (e) will be
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JEE (Main) 2018
MCQ
In a collinear collision, a particle with an initial speed $v_{0}$ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is
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JEE (Main) 2018
MCQ
It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $p_{d}$ ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is $p_{c}$ . The values of $p_{d}$ and $p_{c}$ are respectively
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JEE (Main) 2017
MCQ
A particle $A$ of mass $m$ and initial velocity $\nu$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $\lambda_{A}$ to $\lambda_{B}$ after the collision is
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NEET 2017
MCQ
Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value $10m/s^{2}$ . The work done by the (i) gravitational force and the (ii) resistive force of air is
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JEE (Main) 2017
MCQ
A body of mass $m=10^{-2}kg$ is moving in a medium and experiences a frictional force $F=-kv^{2}$ . Its initial speed is $v_{0}=10ms^{-1}$ . If after 10 s, its energy is $\frac{1}{8}mv_{0}^{2}$ , the value of k will be
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JEE (Main) 2017
MCQ
A time dependent force F=6t acts on a particle of mass 1kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be
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NEET (Phase-II) 2016
MCQ
A particle moves from a point $(-2\hat{i}+5\hat{j})$ to $(4\hat{j}+3\hat{k})$ when a force of $(4\hat{i}+3\hat{j})N$ is applied. How much work has been done by the force
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JEE (Main) 2016
MCQ
A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals $\mu$ . The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other and no energy is lost when particle changes direction from PQ to QR
The values of the coefficient of friction $\mu$ and the distance $x(= QR)$ , are, respectively close to $\wedge P$ .
Surface
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NEET (Phase-II) 2016
MCQ
A bullet of mass 10 g moving horizontally with a velocity of $400 \, ms^{-1}$ strikes of wooden block of mass 2kg which is suspended by a light inextensible string of length 5m. As a result the centre of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be
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JEE (Main) 2016
MCQ
A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times 10^{7} J$ of energy per kg which is converted to mechanical energy with a 20% efficiency rate
(take $g = 9.8 ms^{-2}$ )
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NEET (Phase-I) 2016
MCQ
A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F} = (2\hat{t} + 3t^2\hat{j})N$ , where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and $y$ axis. What power will be developed by the force at the time $t$
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NEET (Phase-II) 2016
MCQ
Two identical balls A and B having velocities of 0.5 m/s and -0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be
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AIPMT (Cancelled) 2015
MCQ
A block of mass 10kg, moving in x direction with a constant speed of $10ms^{-1}$ , is subject to a retarding force F = 0.1x J/m during its travel from x = 20m to 30m. Its final KE will be
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AIPMT (Cancelled) 2015
MCQ
A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time 't' is
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AIPMT 2015
MCQ
The particles A and B, move with constant velocities $\vec{v}_{1}$ . At the initial moment their position vector are $\vec{r}_{1}$ and $\vec{r}_{2}$ respectively. The condition for particles A and B for their collision is
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JEE (Main) 2015
MCQ
A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to
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AIPMT (Cancelled) 2015
MCQ
Two particles of masses $m_{1}, m_{2}$ move with initial velocities $u_{1}$ and $u_{2}$ . On collision, one of the particles get excited to higher level, after absorbing energy $\varepsilon$ if final velocities of particles be $v_{1}$ and $v_{2}$ then we must have
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JEE (Main) 2014
MCQ
When a rubber-band is stretched by a distance $x$ , it exerts a restoring force of magnitude $F = ax + bx^2$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is
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CBSE PMT 2014
MCQ
A body of mass (4m) is lying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is
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JEE (Advanced) 2014
MCQ
A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to the scale
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NEET (Kamataka) 2013
MCQ
A particle with total energy E is moving in a potential energy regions $U(x)$ . Motion of the particle is restricted to the region when
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JEE (Advanced) 2013
MCQ
The work done on a particle of mass m by a force, $K\left[\frac{x}{(x^{2}+y^{2})^{3/2}}\hat{i}+\frac{y}{(x^{2}+y^{2})^{3/2}}\hat{j}\right]$ (K being a constant of appropriate dimensions), when the particle is taken from the point $(a,0)$ to the point $(0,a)$ along a circular path of radius a about the origin in the x-y plane is
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WB-JEE 2013
MCQ
A particle is acted upon by a constant power. Then, which of the following physical quantity remains constant
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AMU (Med.) 2012
MCQ
A particle in a certain conservative force field has a potential energy given by $U = \frac{20xy}{z}$ . The force exerted on it is
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CBSE PMT (Pre.) 2012
MCQ
The potential energy of a particle in a force field is $U = \frac{A}{r^{2}} - \frac{B}{r}$ , where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is
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WB-JEE 2012
MCQ
A spherical ball $A$ of mass $4kg$ , moving along a straight line strikes another spherical ball $B$ of mass $1kg$ at rest. After the collision, $A$ and $B$ move with velocities $v_{1}ms^{-1}$ and $v_{2}ms^{-1}$ respectively making angles of $30^{\circ}$ and $60^{\circ}$ with respect to the original direction of motion of $A$ . The ratio $\frac{v_1}{v_2}$ will be
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CBSE PMT (Pre.) 2012
MCQ
Two spheres $A$ and $B$ of masses $m_{1}$ and $m_{2}$ respectively collide. $A$ is at rest initially and $B$ is moving with velocity $v$ along $x$ -axis. After collision $B$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The mass $A$ moves after collision in the direction
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Kerala PET 2012
MCQ
A girl in a swing is 2.5m above ground at the maximum height and at 1.5m above the ground at the lowest point. Her maximum velocity in the swing is $(g = 10 \, ms^{-2})$
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CBSE PMT (Mains) 2012
MCQ
A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by
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MP PET 2012
MCQ
A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments each of mass m are found to move with a speed 'v' each in mutually perpendicular directions. The total energy released in this process
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CBSE PMT (Mains) 2012
MCQ
A car of mass m starts from rest and accelerates so that instantaneous power delivered to the car has a constant magnitude $P_{0}$ . The instantaneous velocity of this car is proportional to
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Kerala PMT 2012
MCQ
When two spheres of equal masses undergo glancing elastic collision with one of them at rest, after collision they will move
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AMU (Med.) 2012
MCQ
A sphere P of mass m and velocity $\vec{v}_{i}$ undergoes an oblique and perfectly elastic collision with an identical sphere Q initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be
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Kerala PET 2012
MCQ
The shape of the curve representing the relation between the speed and kinetic energy of a moving object is
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Odisha JEE 2011, 12
MCQ
A block of mass 5kg is resting on a smooth surface. At what angle a force of 20N be acted on the body so that it will acquired a kinetic energy of 40J after moving 4m
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CBSE PMT (Pre.) 2011
MCQ
A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest
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Odisha JEE 2011
MCQ
Two masses of $0.25\mathrm{kg}$ each moves towards each other with speed $3\mathrm{ms}^{-1}$ and $1\mathrm{ms}^{-1}$ collide and stick together. Find the final velocity
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Kerala PET 2011
MCQ
A ball dropped from a height of 2m rebounds to a height of 1.5m after hitting the ground. Then the percentage of energy lost is
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IIT-JEE 2011
MCQ
A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is
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CBSE PMT (Pre.) 2011
MCQ
The potential energy of a system increases if work is done
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Kerala PMT 2011
MCQ
Choose the incorrect statement
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Kerala PMT 2010
MCQ
Stopping distance of a moving vehicle is directly proportional to
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AIIMS 2010
MCQ
A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$ . Work done by the cord on the block is
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AIEEE 2010
MCQ
The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$ , where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U(x = \infty) - U_{\mathrm{atequilibrium}}]$ , $D$ is
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J & K CET 2010
MCQ
The energy associated with one gram of mass is
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CBSE PMT 2010
MCQ
An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine
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Kerala PET 2010
MCQ
A force $(4\hat{i} + \hat{j} - 2\hat{k})N$ acting on a body maintains its velocity at $(2\hat{i} + 2\hat{j} + 3\hat{k})ms^{-1}$ . The power exerted is
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AMU (Med.) 2010
MCQ
A billiards player hits a stationary ball by an identical ball to pocket the target ball in a corner pocket that is at an angle of $35^{\circ}$ with respect to the direction of motion of the first ball. Assuming the collision as elastic and that friction and rotational motion are not important, the angle made by the target ball with respect to the incoming ball is
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J & K CET 2010
MCQ
Three identical spherical balls $A, B$ and $C$ are placed on a table as shown in the figure along a straight line. $B$ and $C$ are at rest initially.
The ball A hits B head on with a speed of $10 \, m \, s^{-1}$ . Then after all collisions (assumed to be elastic) A and B are brought to rest and C takes off with a velocity of
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Odisha JEE 2010
MCQ
In an inelastic collision
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CBSE PMT 2010
MCQ
A ball moving with velocity 2 m/s. collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be
Errorless
Kerala PMT 2010
MCQ
The potential energy of a conservative system is given by $V(x) = (x^{2} - 3x)$ joule. Then its equilibrium position is at
Errorless
IIT-JEE 2010
MCQ
A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force $F(t)$ in the x-direction. The force $F(t)$ varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is
Errorless
AIIMS 2010
MCQ
Assertion : The change in kinetic energy of a particle is equal to the work done on it by the net force.
Reason : Change in kinetic energy of particle is equal to the work done only in case of a system of one particle.
Errorless
CBSE PMT 2009
MCQ
A body of mass 1 kg is thrown upwards with a velocity 20 m/s. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction ( $g = 10 \, m/s^{2}$ )
Errorless
AMU PMT 2009
MCQ
A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of $60^{\circ}$ with the vertical with the same initial speed. At highest points of their journey, the ratio of their potential energies will be
Errorless
EAMCET 2009
MCQ
A bullet of mass 0.02 kg travelling horizontally with velocity $250 \, ms^{-1}$ strikes a block of wood of mass 0.23 kg which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of 40m. The coefficient of sliding friction of the rough surface is ( $g = 9.8 \, ms^{-2}$ )
Errorless
EAMCET 2009
MCQ
A motor of power $p_{0}$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe n times, the power of the motor is increased to $p_{1}$ . The ratio of $p_{1}$ to $p_{0}$ is
Errorless
IIT-JEE 2009
MCQ
Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C
Errorless
IIT-JEE 2009
MCQ
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking $g = 10 \, m/s^{2}$ , find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest
Errorless
IIT-JEE 2009
MCQ
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A
Errorless
Kerala PET 2009
MCQ
A particle is acted upon by a force F which varies with position x as shown in figure. If the particle at x = 0 has kinetic energy of 25 J, then the kinetic energy of the particle at $x = 16m$ is
Errorless
KCET 2009
MCQ
The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 m is
Errorless
WB-JEE 2009
MCQ
The force $F$ acting on a particle moving in a straight line is shown in figure. What is the work done by the force on the particle in the $1^{\text{st}}$ meter of the trajectory
$x(\mathrm{in} \mathrm{m}) \longrightarrow$
Errorless
AIEEE 2009
MCQ
Consider a rubber ball freely falling from a height h=4.9m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be
Errorless
DUMET 2009
MCQ
A ball moves in a frictionless inclined table without slipping. The work done by the table surface on the ball is
Errorless
AMU PMT 2009
MCQ
Identify the wrong statement
Errorless
MP PET 2009
MCQ
A neutron travelling with a velocity v and K.E. E collides perfectly elastically head on with the nucleus of an atom of mass number A at rest. The fraction of total energy retained by neutron is
Errorless
WB-JEE 2008
MCQ
A wire is stretched under a force. If the wire suddenly snaps the temperature of the wire
Errorless
Kerala PET 2008
MCQ
Two bodies A and B have masses 20 kg and 5 kg respectively. Each one is acted upon by a force of 4 kg wt. If they acquire the same kinetic energy in times $t_{A}$ and $t_{B}$ , then the ratio $\frac{t_{A}}{t_{B}}$ is
Errorless
Kerala PET 2008
MCQ
A spring gun of spring constant 90 N/cm is compressed 12 cm by a ball of mass 16 g. If the trigger is pulled, the velocity of the ball is
Errorless
Kerala PET 2008
MCQ
A bullet of mass 0.05 kg moving with a speed of $80 \, ms^{-1}$ enters a wooden block and is stopped after a distance of 0.40 m. The average resistive force exerted by the block on the bullet is
Errorless
AIEEE 2008
MCQ
An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range
Errorless
CBSE PMT 2008
MCQ
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine ( $g=10\ m/s^{2}$ )
Errorless
Odisha JEE 2008
MCQ
Two identical mass $M$ moving with velocity $u_{1}$ and $u_{2}$ collide perfectly inelastically. The loss in energy is
Errorless
CBSE PMT 2008
MCQ
A shell of mass 200 gm is ejected from a gun of mass 4kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is
Errorless
AIIMS 2008
MCQ
Assertion : A quick collision between two bodies is more violent than slow collision, even when initial and final velocities are identical.
Reason : The rate of change of momentum determines that force is small or large.
Errorless
Kerala PMT 2007
MCQ
A man pushes a wall and fails to displace it. He does
Errorless
Kerala PET 2007
MCQ
A rod AB of mass 10kg and length 4m rests on a horizontal floor with end A fixed so as to rotate it in vertical plane about perpendicular axis passing through A. If the work done on the rod is 100J, the height to which the end B be raised vertically above the floor is
Errorless
AIEEE 2007
MCQ
A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by
Errorless
Kerala PET 2007
MCQ
A particle is released from a height S. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively
Errorless
Kerala PET 2007
MCQ
A simple pendulum is released from $A$ as shown. If $m$ and $l$ represent the mass of the bob and length of the pendulum, the gain in kinetic energy at $B$ is
Errorless
Kerala PET 2007
MCQ
An electric pump is used to fill an overhead tank of capacity $9m^{3}$ kept at a height of 10m above the ground. If the pump takes 5 minutes to fill the tank by consuming 10kW power the efficiency of the pump should be (Take $g = 10ms^{-2}$ )
Errorless
KCET 2007
MCQ
A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2:3. The smaller fragment moves with a velocity of $6 \, ms^{-1}$ . The kinetic energy of the larger fragment is
Errorless
GUJCET 2007
MCQ
A nucleus at rest splits into two nuclear parts having same density and radii in the ratio 1:2. Their velocities are in the ratio
Errorless
AIEEE 2006
MCQ
A particle of mass 100g is thrown vertically upwards with a speed of 5m/s. The work done by the force of gravity during the time the particle goes up is
Errorless
AFMC 2006
MCQ
The area of the acceleration-displacement curve of a body gives
Errorless
AFMC 2006
MCQ
If we throw a body upwards with velocity of 4 m/s, at what height does its kinetic energy reduce to half of the initial value (Taking $g = 10 \, ms^{-1}$ )
Errorless
Kerala PMT 2006
MCQ
The slope of the kinetic energy versus position vector gives the rate of change of
Errorless
J & K CET 2006
MCQ
A body at rest breaks into two pieces with unequal mass
Errorless
J & K CET 2006
MCQ
A body of mass 2 kg is projected at 20 m/s at an angle $60^{\circ}$ above the horizontal. Power on the block due to the gravitational force at its highest point is
Errorless
BHU 2006
MCQ
A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to
Errorless
DCE 2006
MCQ
An intense stream of water of cross-sectional area A strikes a wall at an angle $\theta$ with the normal to the wall and returns back elastically. If the density of water is $\rho$ and its velocity is v, then the force exerted in the wall will be
Errorless
MP PMT 2006
MCQ
A body of mass ‘M’ collides against a wall with a velocity v and retraces its path with the same speed. The change in momentum is (take initial direction of velocity as positive)
Errorless
AIEEE 2006
MCQ
A mass of $Mkg$ is suspended by a weightless string. the horizontal force that is required to displace it until the string makes an angle of $45^{\circ}$ with the initial vertical direction is
Errorless
AIEEE 2006
MCQ
The potential energy of a 1 kg particle free to move along the x-axis is given by
$V (x) = \left(\frac {x ^ {4}}{4} - \frac {x ^ {2}}{2}\right) J$
The total mechanical energy of the particle is 2 J. Then, the maximum speed (in m/s) is
Errorless
Kerala PET 2005
MCQ
A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is
Errorless
Kerala PMT 2005
MCQ
Which one of the following is not a conservative force
Errorless
AIEEE 2005
MCQ
The block of mass $M$ moving on the frictionless horizontal surface collides with the spring of spring constant $K$ and compresses it by length $L$ . The maximum momentum of the block after collision is
Errorless
AIEEE 2005; AIIMS 2007
MCQ
A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It slides down a smooth surface to the ground, then climbs up another hill of height 30 m and finally slides down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is
Errorless
RPMT 2005
MCQ
An electric immersion heater of 1.08 kW is immersed in water. After the water has reached a temperature of $100^{\circ}$ C, how much time will be required to produce 100g of steam
Errorless
RPMT 2005
MCQ
An apple gives 21 kJ energy to a boy. How much height he can climb by using this energy if his efficiency is 28% (mass of boy = 40 kg)
Errorless
J & K CET 2005
MCQ
If the heart pushes 1 cc of blood in one second under pressure $20000N / m^2$ the power of heart is
Errorless
J & K CET 2005; NEET (Karnataka) 2013
MCQ
A man does a given amount of work in 10 sec. Another man does the same amount of work in 20 sec. The ratio of the output power of first man to the second man is
Errorless
AIEEE 2005; AIPMT 2015
MCQ
On a frictionless surface a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle $\theta$ to its initial direction and has a speed $\frac{v}{3}$ . The second block's speed after the collision is
Errorless
KCET 2005; Kerala PET 2009
MCQ
The relationship between the force F and position x of a body is as shown in figure. The work done in displacing the body from x = 1 m to x = 5 m will be
Errorless
CBSE PMT 2005
MCQ
A force $F$ acting on an object varies with distance $x$ as shown here. The force is in newton and $x$ in metre. The work done by the force in moving the object from $x = 0$ to $x = 6m$ is
Errorless
AIEEE 2004
MCQ
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that
Errorless
DCE 2004
MCQ
A man starts walking from a point on the surface of earth (assumed smooth) and reaches diagonally opposite point. What is the work done by him
Errorless
BCECE 2004
MCQ
A ball of mass m moves with speed v and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is
Errorless
AIEEE 2004
MCQ
A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
Errorless
DCE 2004
MCQ
Natural length of a spring is 60 cm, and its spring constant is 4000 N/m. A mass of 20 kg is hung from it. The extension produced in the spring is, (Take $g = 9.8 \, m/s^{2}$ )
Errorless
AFMC 2004; Odisha JEE 2008
MCQ
A rifle bullet loses $1/20^{th}$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is
Errorless
Pb. PET 2004
MCQ
If a shell fired from a cannon, explodes in mid air, then
Errorless
DCE 2004
MCQ
A body is moving with a velocity v, breaks up into two equal parts. One of the part retraces back with velocity v. Then the velocity of the other part is
Errorless
CBSE PMT 2004
MCQ
A ball of mass 2kg and another of mass 4kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio of
Errorless
KCET 2004
MCQ
A bullet moving with a speed of $100 \, ms^{-1}$ can just penetrate two planks of equal thickness. Then the number of such planks penetrated by the same bullet when the speed is doubled will be
Errorless
AIIMS 2004
MCQ
A bomb of mass 3.0 kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 80 m/s. The total energy imparted to the two fragments is
Errorless
DCE 2004
MCQ
A bomb is kept stationary at a point. It suddenly explodes into two fragments of masses 1 g and 3 g. The total K.E. of the fragments is $6.4 \times 10^{4} J$ . What is the K.E. of the smaller fragment
Errorless
UPSEAT 2004
MCQ
An object of mass 3m splits into three equal fragments. Two fragments have velocities $v\hat{j}$ and $v\hat{i}$ . The velocity of the third fragment is
Errorless
Odisha PMT 2004
MCQ
Four particles given, have same momentum. Which has maximum kinetic energy
Errorless
AIEEE 2004; BHU 2006
MCQ
A body of mass m accelerates uniformly from rest to $v_{1}$ in time $t_{1}$ . As a function of time t, the instantaneous power delivered to the body is
Errorless
Kerala PMT 2004
MCQ
Power of a water pump is 2 kW. If $g = 10 \, m/sec^{2}$ , the amount of water it can raise in one minute to a height of 10 m is
Errorless
Odisha PMT 2004
MCQ
A shell initially at rest explodes into two pieces of equal mass, then the two pieces will
Errorless
DCE 2004
MCQ
Two balls at same temperature collide. What is conserved
Errorless
Odisha PMT 2004
MCQ
A body of mass m is at rest. Another body of same mass moving with velocity V makes head on elastic collision with the first body. After collision the first body starts to move with velocity
Errorless
UPSEAT 2004
MCQ
Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of 0.4 m/s. It collides head on with the second elastically, the second one similarly with the third and so on. The velocity of the last ball is
Errorless
BCECE 2004; J & K CET 2006
MCQ
A body of mass M moves with velocity v and collides elastically with a another body of mass m (M>>m) at rest then the velocity of body of mass m is
Errorless
UPSEAT 2004
MCQ
Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision the projectile and the struck particle move in directions making angles $\theta_{1}$ and $\theta_{2}$ respectively with the initial direction of motion. The sum of the angles. $\theta_{1} + \theta_{2}$ , is
Errorless
IIT-JEE (Screening) 2004; J & K CET 2006
MCQ
A particle is placed at the origin and a force $F = kx$ is acting on it (where $k$ is positive constant). If $U(0) = 0$ , the graph of $U(x)$ versus $x$ will be (where $U$ is the potential energy function)
Errorless
MP PET 2003
MCQ
A body of mass 5 kg is placed at the origin, and can move only on the x-axis. A force of 10 N is acting on it in a direction making an angle of $60^{\circ}$ with the x-axis and displaces it along the x-axis by 4 metres. The work done by the force is
Errorless
BCECE 2003
MCQ
A spring when stretched by 2 mm its potential energy becomes 4 J. If it is stretched by 10 mm, its potential energy is equal to
Errorless
CBSE PMT 2003; KCET 2012
MCQ
A stationary particle explodes into two particles of a masses $m_{1}$ and $m_{2}$ which move in opposite directions with velocities $v_{1}$ and $v_{2}$ . The ratio of their kinetic energies $E_{1}/E_{2}$ is
Errorless
MP PET 2003
MCQ
The potential energy of a weight less spring compressed by a distance $a$ is proportional to
Errorless
Pb. PET 2003
MCQ
From an automatic gun a man fires 360 bullet per minute with a speed of 360 km/hour. If each weighs 20 g, the power of the gun is
Errorless
EAMCET 2003
MCQ
Two particles having position vectors $\vec{r}_1 = (3\hat{i} + 5\hat{j})$ metres and $\vec{r}_2 = (-5\hat{i} - 3\hat{j})$ metres are moving with velocities $\vec{v}_1 = (4\hat{i} + 3\hat{j})m / s$ and $\vec{v}_2 = (\alpha \hat{i} + 7\hat{j}) m / s$ . If they collide after 2 seconds, the value of ' $\alpha'$ is
Errorless
Pb. PET 2003
MCQ
Two bodies of masses 0.1 kg and 0.4 kg move towards each other with the velocities 1 m/s and 0.1 m/s respectively, After collision they stick together. In 10 sec the combined mass travels
Errorless
IIT-JEE (Screening) 2003
MCQ
If $W_{1}, W_{2}$ and $W_{3}$ represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between $W_{1}, W_{2}$ and $W_{3}$
Errorless
MP PMT 2003
MCQ
A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then
Errorless
AIEEE 2003
MCQ
Consider the following two statements
1 Linear momentum of a system of particles is zero
2 Kinetic energy of a system of particles is zero,
Then
Errorless
AFMC 2002
MCQ
If force and displacement of particle in direction of force are doubled. Work would be
Errorless
AFMC 2002
MCQ
Which of the following is a unit of energy
Errorless
JIPMER 2002
MCQ
A 50kg man with 20kg load on his head climbs up 20 steps of 0.25m height each. The work done in climbing is
Errorless
DCE 2002; Odisha JEE 2005; Kerala PMT 2006; Kerala PET 2008
MCQ
A particle moves under the effect of a force $F = Cx$ from $x = 0$ to $x = x_{1}$ . The work done in the process is
Errorless
Odisha JEE 2002; Kerala PMT 2006
MCQ
A position dependent force $F=7-2x+3x^{2}$ newton acts on a small body of mass 2 kg and displaces it from x=0 to x=5m. The work done in joules is
Errorless
Odisha JEE 2002
MCQ
When a spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2 cm, the stored energy will be increased by
Errorless
AIEEE 2002, 03
MCQ
A spring of spring constant $5 \times 10^{3}$ N/m is stretched initially by 5cm from the unstretched position. Then the work required to stretch it further by another 5cm is
Errorless
MP PMT 2002; CBSE PMT 2003, 06; UPSEAT 2004; Odisha PMT 2004; WB-JEE 2012
MCQ
If a long spring is stretched by 0.02 m, its potential energy is U. If the spring is stretched by 0.1 m, then its potential energy will be
Errorless
MP PET 2002
MCQ
In an explosion a body breaks up into two pieces of unequal masses. In this
Errorless
RPET 2002
MCQ
A particle of mass m moving with velocity $V_{0}$ strikes a simple pendulum of mass m and sticks to it. The maximum height attained by the pendulum will be
Errorless
Kerala PET 2002
MCQ
A particle of mass m at rest is acted upon by a force F for a time t. Its kinetic energy after an interval t is
Errorless
BHU 2002
MCQ
Two bodies moving towards each other collide and move away in opposite directions. There is some rise in temperature of bodies because a part of the kinetic energy is converted into
Errorless
Pb. PET 2002
MCQ
If a man increase his speed by 2 m/s, his K.E. is doubled, the original speed of the man is
Errorless
Kerala PMT 2002
MCQ
A machine which is 75 percent efficient, uses 12 joules of energy in lifting up a $1\mathrm{kg}$ mass through a certain distance. The mass is then allowed to fall through that distance. The velocity at the end of its fall is (in $ms^{-1}$ )
Errorless
AIEEE 2002; DCE 2002; BCECE 2006; WB-JEE 2012
MCQ
If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest
Errorless
Pb. PMT 2002; J & K CET 2004
MCQ
A body moving with velocity v has momentum and kinetic energy numerically equal. What is the value of v
Errorless
JIPMER 2002
MCQ
A pump motor is used to deliver water at a certain rate from a given pipe. To obtain twice as much water from the same pipe in the same time, power of the motor has to be increased to
Errorless
Kerala PET 2002
MCQ
A quarter horse power motor runs at a speed of 600 r.p.m. Assuming 40% efficiency the work done by the motor in one rotation will be
Errorless
Kerala PET 2002; CBSE PMT (Mains) 2010
MCQ
A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is
Errorless
Kerala PET 2002; EAMCET 2009
MCQ
A body of mass 2kg makes an elastic collision with another body at rest and continues to move in the original direction with one fourth of its original speed. The mass of the second body which collides with the first body is
Errorless
AFMC 2002; RPMT 2003
MCQ
Two masses $m_A$ and $m_B$ moving with velocities $v_A$ and $v_B$ in opposite directions collide elastically. After that the masses $m_A$ and $m_B$ move with velocity $v_B$ and $v_A$ respectively. The ratio $(m_A / m_B)$ is
Errorless
Kerala PMT 2002; MP PET 2002; WB-JEE 2013
MCQ
A bullet of mass m moving with velocity v strikes a block of mass M at rest and gets embedded into it. The kinetic energy of the composite block will be
Errorless
IIT-JEE (Screening) 2002; DCE 2006
MCQ
A particle which is constrained to move along the $x$ -axis, is subjected to a force in the same direction which varies with the distance $x$ of the particle from the origin as $F(x) = -kx + ax^3$ . Here $k$ and $a$ are positive constants. For $x \geq 0$ , the functional from of the potential energy $U(x)$ of the particle is
Errorless
MP PMT 2001; CBSE PMT 2004
MCQ
A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 N/m and comes to rest after compressing the spring. The compression of the spring is
Errorless
BCECE 2001; CBSE PMT 2007; AIIMS 2008;
!
MCQ
A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$ . The net work done in the process is (images/be8937a3a0433e0f15a44a7540122b8cc89d7a194dca520d0cde82c3001f4c94.jpg)
Errorless
Kerala (Engg.) 2001; EAMCET 2001; DPMT 2004; UP CPMT 2006
MCQ
A truck of mass 30,000kg moves up an inclined plane of slope 1 in 100 at a speed of 30 kmph. The power of the truck is (Given $g = 10ms^{-2}$ )
Errorless
DCE 2001, 02; Odisha JEE 2002
MCQ
A body of mass $M_{1}$ collides elastically with another mass $M_{2}$ at rest. There is maximum transfer of energy when
Errorless
UPSEAT 2001; EAMCET 2009
MCQ
A body at rest breaks up into 3 parts. If 2 parts having equal masses fly off perpendicularly each after with a velocity of $12m/s$ , then the velocity of the third part which has 3 times mass of each part is
Errorless
UPSEAT 2000; CPMT 2002; Pb. PET 2004; MP PMT 2012
MCQ
The potential energy of a certain spring when stretched through a distance ‘S’ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ‘S’ will be
Errorless
MHCET 2000; Kerala PMT 2008; AMU PMT 2009; AIPMT (Cancelled) 2015
MCQ
Two similar springs P and Q have spring constants $K_{P}$ and $K_{Q}$ , such that $K_{P} > K_{Q}$ . They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs $W_{P}$ and $W_{Q}$ are related as, in case (a) and case (b), respectively
Errorless
DPMT 2000; Odisha JEE 2005
MCQ
A mass of 100g strikes the wall with speed 5m/s at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 \times 10^{-3}$ sec, what is the force applied on the mass by the wall
Errorless
AFMC 1999; Pb. PMT 2003
MCQ
The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of $15^{\circ}$ with the horizontal is $[\sin15^{\circ}=0.2588]$
Errorless
RPMT 1999; DCE 2003
MCQ
A space craft of mass 'M' and moving with velocity 'v' suddenly breaks in two pieces of same mass m. After the explosion one of the mass 'm' becomes stationary. What is the velocity of the other part of craft
Errorless
IIT-JEE 1999; UPSEAT 2003
MCQ
A particle free to move along the x-axis has potential energy given by $U(x)=k\left[1-\exp\left(-x\right)^{2}\right]$ for $-\infty\leq x\leq+\infty$ , where k is a positive constant of appropriate dimensions. Then
Errorless
RPET 1999, 2001; UPSEAT 2002
MCQ
A shell is fired from a cannon with velocity v m/sec at an angle $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed in m/sec of the other piece immediately after the explosion is
Errorless
CBSE PMT 1998; Kerala PET 2012
MCQ
A force acts on a 30 g particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^{2} + t^{3}$ , where x is in metres and t is in seconds. The work done during the first 4 seconds is
Errorless
MP PMT/PET 1998; Pb. PMT 2002
MCQ
Two springs of spring constants 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in the ratio
Errorless
BHU 1998; EAMCET 2001; CBSE PMT 2006; WB-JEE 2008
MCQ
A body of mass 3 kg is under a force, which causes a displacement in it given by $S = \frac{t^{3}}{3}$ (in m). Find the work done by the force in first 2 seconds
Errorless
AIIMS 1998; UPSEAT 2000; JIPMER 2001; Kerala PMT 2004
MCQ
A light and a heavy body have equal momenta. Which one has greater K.E
Errorless
AIIMS 1998, 2002; KCET 2000; CPMT 2003; J & K CET 2004; Kerala PMT 2005; RPMT 2006
MCQ
If the K.E. of a particle is doubled, then its momentum will
Errorless
AFMC 1998; RPMT 1999; DPMT 2000; MP PET 2004
MCQ
The kinetic energy of a body of mass 3 kg and momentum 2 Ns is
Errorless
BHU 1998, 2005; JIPMER 2001, 02; AFMC 2005
MCQ
Which of the following is not a perfectly inelastic collision
Errorless
JIPMER 1997; CBSE PMT 1999; BHU 2000; RPMT 2000; Odisha JEE 2002
MCQ
A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done is 25 joules, the angle which the force makes with the direction of motion of the body is
Errorless
MP PMT 1997, 2000; JIPMER 2000; AIEEE 2002, 04; DCE 2006
MCQ
A uniform chain of length 2m is kept on a table such that a length of 60cm hangs freely from the edge of the table. The total mass of the chain is 4kg. What is the work done in pulling the entire chain on the table
Errorless
MP PMT 1997; CPMT 1997; DPMT 2001
MCQ
If a lighter body (mass $M_{1}$ and velocity $V_{1}$ ) and a heavier body (mass $M_{2}$ and velocity $V_{2}$ ) have the same kinetic energy, then
Errorless
BHU 1997; MP PET 2000; CBSE PMT 2000; MH CET 2000; JIPMER 2001, 02; AMU (Med.) 2002; DPMT 2003
MCQ
The power of a pump, which can pump 200kg of water to a height of 200m in 10sec is $(g=10m/s^{2})$
Errorless
MP PMT 1997; CBSE PMT 1998; AIIMS 2000; UPSEAT 2001; MP PET 2001, 02, 07; Kerala PMT 2008
MCQ
Two equal masses $m_{1}$ and $m_{2}$ moving along the same straight line with velocities +3 m/s and -5 m/s respectively collide elastically. Their velocities after the collision will be respectively
Errorless
CPMT 1997; MP PET 1999; DPMT 1999, 2005; JIPMER 2000
MCQ
A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity
Errorless
CBSE PMT 1997; AIIMS 2001; Pb. PMT 2001; J & K CET 2005; AIEEE 2008
MCQ
A body of mass 4 kg moving with velocity 12 m/s collides with another body of mass 6 kg at rest. If two bodies stick together after collision, then the loss of kinetic energy of system is
Errorless
BHU 1997; J & K CET 2010; CBSE PMT (Pre.) 2011
MCQ
Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m
Errorless
CBSE PMT 1996; MP PMT/PET 1998; AIIMS 1999; JIPMER 2001, 02; RPMT 2005
MCQ
A particle of mass m moving with velocity v strikes a stationary particle of mass 2m and sticks to it. The speed of the system will be
Errorless
Haryana CEE 1996; BVP 2003
MCQ
Two putty balls of equal mass moving with equal velocity in mutually perpendicular directions, stick together after collision. If the balls were initially moving with a velocity of $45\sqrt{2} ms^{-1}$ each, the velocity of their combined mass after collision is
Errorless
AFMC 1996, 2006; BHU 2001; DCE 2004, 09; AIIMS 2006; UP CPMT 2006
MCQ
In an inelastic collision, what is conserved
Errorless
EAMCET (Engg.) 1995; WB-JEE 2009
MCQ
Two bodies of masses 2m and m have their K.E. in the ratio 8:1, then their ratio of momenta is
Errorless
Manipal MEE 1995; AIEEE 2002, 06; Pb. PET 2004; CBSE PMT 2005; KCET 2007; Odisha JEE 2008
MCQ
A bomb of mass 9kg explodes into 2 pieces of mass 3kg and 6kg. The velocity of mass 3kg is 1.6 m/s, the K.E. of mass 6kg is
Errorless
CBSE PMT 1995; AIEEE 2003
MCQ
A $^{238}U$ nucleus decays by emitting an alpha particle of speed $v \, ms^{-1}$ . The recoil speed of the residual nucleus is (in $ms^{-1}$ )
Errorless
BHU 1995; MP PET 1996; AMU (Med.) 1999; JIPMER 2000; JEE (Main) 2021
MCQ
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to
Errorless
MCQ
A wire, which passes through the hole is a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead
Errorless
MCQ
A body of mass M is moving with a uniform speed of 10m/s on frictionless surface under the influence of two forces $F_{1}$ and $F_{2}$ . The net power of the system is
Errorless
MCQ
A ball is thrown vertically downwards from a height of 20 m with an initial velocity $v_{0}$ . It collides with the ground loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity $v_{0}$ is (Take $g = 10 ms^{-2}$ )
Errorless
MCQ
Two particles of equal mass m have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right)$ . They collide completely inelastically. The energy lost in the process is
Errorless
MCQ
Assertion : If two protons are brought near one another, the potential energy of the system will increase.
Reason : The charge on the proton is $+1.6 \times 10^{-19} C$ .
Errorless
MCQ
Assertion : Mass and energy are not conserved separately, but are conserved as a single entity called mass-energy.
Reason : Mass and energy conservation can be obtained by Einstein equation for energy.
Errorless
MCQ
Assertion : Work done by friction on a body sliding down an inclined plane is positive.
Reason : Work done is greater than zero, if angle between force and displacement is acute or both are in same direction.
Errorless
MCQ
A horizontal force of 5 N is required to maintain a velocity of 2 m/s for a block of 10 kg mass sliding over a rough surface. The work done by this force in one minute is
Errorless
MCQ
Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by
Errorless
MCQ
When a body moves with some friction on a surface
Errorless
MCQ
A bullet of mass m moving with velocity v strikes a suspended wooden block of mass M. If the block rises to a height h, the initial velocity of the block will be
Errorless
MCQ
The slope of kinetic energy displacement curve of a particle in motion is
Errorless
MCQ
The energy required to accelerate a car from 10 m/s to 20 m/s is how many times the energy required to accelerate the car from rest to 10 m/s
Errorless
MCQ
A body of mass 2 kg slides down a curved track which is quadrant of a circle of radius 1 metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is
Errorless
MCQ
A bomb of mass 3m kg explodes into two pieces of mass m kg and 2m kg. If the velocity of m kg mass is 16 m/s, the total kinetic energy released in the explosion is
Errorless
MCQ
Identify the false statement from the following