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Work, Power & Energy

769 Questions Start Allen Test
All Exams Allen Advance Errorless
Q376 Allen Work Energy Theorem MCQ
A small object with mass $m = 2 \, kg$ is attached to the free end of an ideal spring with $k = 10 \, Nm^{-1}$ . The other end of the spring is connected to a fixed frictionless pivot located at the origin $O$ as shown in the Figure. The relaxed length of the spring is $1 \, m$ . An unspecified force $F$ carries the object at rest from point $A$ to point $B$ . At point $B$ , the object has the speed $5 \, ms^{-1}$ . The work done by the force $F$ is (Neglect gravity):-
A.
$130 \, J$
B.
$80 \, J$
C.
$-105 \, J$
D.
$-80 \, J$
Q377 Allen Work Energy Theorem MCQ
In the arrangement shown a block of mass 2kg is pressed against a spring which is compressed by 10 cm and is applying a force of 80 N to the block. The spring is not attached to the block. The coefficient of friction is 0.5. When the block is released it moves up the plane by some distance and then comes back down. The kinetic energy of the block just before it starts compressing the spring again is
A.
$2J$
B.
$1.6J$
C.
$0.8J$
D.
$0.4J$
Q378 Allen Work Energy Theorem MCQ
A block of mass 10kg is attached to a relaxed spring. Other end is attached to ceiling and block is released keeping the spring in vertical position. The spring is such that it has elongation of 10 cm under a force of 100 N. The maximum velocity of block in subsequent motion is:-
A.
1 m/s
B.
1.5 m/s
C.
2.0 m/s
D.
2.5 m/s
Q379 Allen Work Energy Theorem MCQ
A light spring of length 20 cm and force constant 2 N/cm is placed vertically on a table. A small block of mass 1 kg falls on it. The length h from the surface of the table at which the block will have the maximum velocity is:
A.
20 cm
B.
15 cm
C.
10 cm
D.
5cm
Q380 Allen Work Energy Theorem MCQ
In the figure shown, the system is released from rest. Find the velocity of block A when block B has fallen a distance ' $\ell'$ . Assume all pulleys to be massless and frictionless.
A.
$\sqrt{\frac{g\ell}{5}}$
B.
$\sqrt{g\ell}$
C.
$\sqrt{5g\ell}$
D.
None of these
Q381 Allen Work Energy Theorem Match the Columns
Two blocks, of masses M and 2M, are connected to a light spring of spring constant K that has one end fixed, as shown in figure. The horizontal surface and the pulley are frictionless. The blocks are released from rest when the spring is non deformed. The string is light.
Column-IColumn-II
(A)I and IV
(B)I and II
(C)III and IV
(D)None of these
(I)Maximum extension in the spring is $\frac{4Mg}{K}$
(II)Maximum kinetic energy of the system is $\frac{2M^{2}g^{2}}{K}$ .
(III)Maximum extension in the spring is $\frac{2Mg}{K}$ .
(IV)Maximum kinetic energy of the system is $\frac{4M^{2}g^{2}}{K}$ . Then which of the following option is correct?
Q382 Allen Potential Energy MCQ
A radial force $\vec{F} = \frac{A}{r^2}\hat{r}$ acts on a particle. The work done by the force in displacing a particle from (1, 0) to (3, 4) is:
A.
$\frac{A}{5}$
B.
$\frac{A}{2}$
C.
$\frac{4A}{5}$
D.
$\frac{4A}{3}$
Q383 Allen Potential Energy MCQ
When a conservative force does positive work on a body
A.
the potential energy increases
B.
the potential energy decreases
C.
total energy increases
D.
total energy decreases
Q384 Allen Potential Energy MCQ
A wedge of mass M fitted with a spring of stiffness 'k' is kept on a smooth horizontal surface. A rod of mass m is kept on the wedge as shown in the figure. System is in equilibrium. Assuming that all surfaces are smooth, the potential energy stored in the spring is:
A.
$\frac{mg^2\tan^2\theta}{2k}$
B.
$\frac{m^2g\tan^2\theta}{2k}$
C.
$\frac{m^2g^2\tan^2\theta}{2k}$
D.
$\frac{m^2g^2\tan^2\theta}{k}$
Q385 Allen Potential Energy MCQ
A body with mass 2 kg moves in one direction in the presence of a force which is described by the potential energy graph. If the body is released from rest at x = 2m, then its speed when it crosses x = 5 m is
A.
zero
B.
$1ms^{-1}$
C.
$2ms^{-1}$
D.
$3ms^{-1}$
Q386 Allen Potential Energy MCQ
The potential energy between two atoms in a molecule is given by $U = ax^{3} - bx^{2}$ where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when x is equal to :-
A.
0
B.
$\frac{2b}{3a}$
C.
$\frac{3a}{2b}$
D.
$\frac{3b}{2a}$
Q387 Allen Potential Energy MCQ
A conservative force $\vec{F}=(4x-8)\hat{i}N$ acts on a particle that moves on the x-axis. The potential energy associated with this force is assigned a value of 8J at x=0. Which of the following best represents variation in potential energy with position coordinate x?
A.
B.
C.
D.
Q388 Allen Potential Energy MCQ
Potential energy curve U of a particle as function of the position of a particle is shown. The particle has total mechanical energy E of 3.0 joules.
A.
It can never be present at x = 0 m.
B.
It can never be present at x = 5 m
C.
At x = 2 its kinetic energy is 0 J
D.
At x = 1 its kinetic energy 3 J
Q389 Allen Potential Energy MCQ
The potential energy $U(x)$ of a particle moving along x-axis is shown in figure. Which one of the following graphs represents the variation of kinetic energy of this particle if its total mechanical energy is $E_{0}$ ?
A.
B.
C.
D.
Q390 Allen Motion in Vertical Circle MCQ
A stone is tied to a string of length 2 m is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed 10 m/s. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is
A.
$\sqrt{60}$
B.
$\sqrt{40}$
C.
$\sqrt{80}$
D.
$\sqrt{160}$
Q391 Allen Motion in Vertical Circle MCQ
A small block slides down from rest at point A on the surface of a smooth circular cylinder, as shown. At point B, the block falls off (leaves) the cylinder. The equation relating the angles $\theta_{1}$ and $\theta_{2}$ is given by
A.
$\sin \theta_{2} = \frac{2}{3}\sin \theta_{1}$
B.
$\sin \theta_{2} = \frac{3}{2}\sin \theta_{1}$
C.
$\cos \theta_{2} = \frac{2}{3}\cos \theta_{1}$
D.
$\cos \theta_{2} = \frac{3}{2}\cos \theta_{1}$
Q392 Allen Motion in Vertical Circle MCQ
A particle of mass m is connected from a light inextensible string of length $\ell$ such that it behaves as a simple pendulum. Now string is pulled to point A making an angle $\theta_{1}$ with the vertical and it is released from the point A then.
A.
Speed of the particle when string makes an angle $\theta_{2}$ with vertical, is $\sqrt{2g\ell(cos\theta_{2}-cos\theta_{1})}$
B.
Speed of the particle when string makes an angle $\theta_{2}$ with vertical, is $\sqrt{g\ell(cos\theta_2 - cos\theta_1)}$
C.
The tension in the string when string makes an angle $\theta_{2}$ with vertical is $mg$ ( $4\cos\theta_{2}-2\cos\theta_{1}$ )
D.
The tension in the string when string makes an angle $\theta_{2}$ with vertical is $mg\left(\cos\theta_{2}-\cos\theta_{1}\right)$
Q393 Allen Motion in Vertical Circle MCQ
A stone of mass m at the end of a string of length L is whirled in a vertical circle at a constant speed. The tension in the string will be maximum when the stone is
A.
At the top of the circle
B.
Half way down from the top
C.
Quarter way down from the top
D.
At the bottom of the circle
Q394 Allen Motion in Vertical Circle MCQ
Two bodies of mass m and 4m are attached to a string as shown in the figure. The body of mass m hanging from string is executing oscillation with angular amplitude $60^{\circ}$ while other body is at rest on a horizontal surface. The minimum coefficient of friction between the mass 4m and the horizontal surface is :
A.
$1 / 4$
B.
$3 / 4$
C.
$1 / 2$
D.
$1 / 8$
Q395 Allen Motion in Vertical Circle MCQ
As shown in figure BEF is a fixed vertical circular tube. A block of mass m starts moving in the tube at point B with velocity V towards E. It is just able to complete the vertical circle, then choose the INCORRECT option :-
A.
velocity at B must be $\sqrt{3Rg}$
B.
velocity at F must be $\sqrt{2Rg}$
C.
normal reaction at point F is 2mg
D.
the normal reaction at point E is 6 mg
Q396 Allen Power MCQ
A body of mass m accelerates uniformly from rest to $v_{1}$ in time $t_{1}$ . The instantaneous power delivered to the body as a function of time t is-
A.
$\frac{mv_{1}t}{t_{1}}$
B.
$\frac{mv_{1}^{2}t}{t_{1}^{2}}$
C.
$\frac{mv_{1}t^{2}}{t_{1}}$
D.
$\frac{mv_{1}^{2}t}{t_{1}}$
Q397 Allen Power MCQ
Assume the aerodynamic drag force on a car is proportional to its speed. If the power output from the engine is doubled, then the maximum speed of the car.
A.
is unchanged
B.
increases by a factor of $\sqrt{2}$
C.
is also doubled
D.
increases by a factor of four
Q398 Allen Power MCQ
A particle (bob) of mass 1 kg is performing vertical circular motion. Then :
A.
Power delivered by tension at point 4) is negative.
B.
Power delivered by tension at point 2) is positive.
C.
Power delivered by gravitational force at point 3) is zero
D.
Power delivered by gravitational force at point 4) is negative.
Q399 Allen Kinematics of Circular Motion MSQ
A particle is moving along a circular path as shown in figure below. The instantaneous velocity of the particle is $\vec{v}=(4m/s)\hat{i}-(3\mathrm{~m/s})\hat{j}$ . The particle may be moving through
A.
first quadrant
B.
second quadrant
C.
third quadrant
D.
fourth quadrant
Q400 Allen Kinematics of Circular Motion MSQ
The second-hand of a tower clock is 1.00 m long. Which of the following is/are CORRECT statement(s).
A.
Linear velocity of the tip of the hand is $\frac{10\pi}{3} cm / s$ .
B.
Angular velocity of the hand is $\frac{\pi}{30} rad / s$ .
C.
Average acceleration of the tip of the hand in 15 minutes is zero.
D.
Instantaneous acceleration of the tip of the hand is $\frac{\pi^2}{9} cm / s^2$ .