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Work, Power & Energy

238 Questions Start Errorless Test
All Exams Allen Advance Errorless
JEE (Advanced) 2017 Q101 Errorless 9. JEE Section MSQ
A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x=0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and its slides down. When the mass loses contact with the block, its position is x and the velocity is v. At the instant, which of the following options is/are correct
A.
The velocity of the point mass $m$ is: $v = \sqrt{\frac{2gR}{1 + \frac{m}{M}}}$
B.
The $x$ component of displacement of the center of mass of the block $M$ is: $-\frac{mR}{M + m}$
C.
The position of the point mass is: $x = -\sqrt{2}\frac{mR}{M + m}$
D.
The velocity of the block $M$ is: $V = -\frac{m}{M}\sqrt{2gR}$
JEE (Main) 2016 Q102 Errorless 3. Conservation of Energy and Momentum 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 $\mathbf{P}_{\bullet}$ .
A.
0.2 and $3.5m$
B.
0.29 and $3.5m$
C.
0.29 and $6.5m$
D.
0.2 and $6.5m$
NEET (Phase-II) 2016 Q103 Errorless 3. Conservation of Energy and Momentum 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
A.
$160 \, ms^{-1}$
B.
$100 \, ms^{-1}$
C.
$80 \, ms^{-1}$
D.
$120 \, ms^{-1}$
JEE (Main) 2016 Q104 Errorless 3. Conservation of Energy and Momentum MCQ
A person trying to lose weight by burning fat lifts a mass of 10 kg up to 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 $g = 9.8 ms^{-2}$ )
A.
$6.45 \times 10^{-3} kg$
B.
$9.89 \times 10^{-3} kg$
C.
$12.89 \times 10^{-3} kg$
D.
$2.45 \times 10^{-3} kg$
NEET (Phase-II) 2016 Q105 Errorless 5. Elastic and Inelastic Collision 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
A.
0.3 m/s and 0.5 m/s
B.
-0.5 m/s and 0.3 m/s
C.
0.5 m/s and -0.3 m/s
D.
-0.3 m/s and 0.5 m/s
JEE (Main) 2015 Q106 Errorless 5. Elastic and Inelastic Collision 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
A.
44%
B.
50%
C.
56%
D.
62%
JEE (Advanced) 2015 Q107 Errorless 9. JEE Section Numerical
Two identical uniform discs roll without slipping on two different surfaces AB and CD (see figure) starting at A and C with linear speeds $v_{1}$ and $v_{2}$ , respectively and always remain in contact with the surfaces. If they reach B and D with the same linear speed and $v_{1}=3m/s$ , then $v_{2}$ in m/s is $(g=10\ m/s^{2})$
JEE (Advanced) 2015 Q108 Errorless 10. Matrix Match Type Questions Numerical
A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in Column-I (a and $U_{0}$ are constants). Match the potential energies in column I to the corresponding statement
Column-IColumn-II
(A)$U_1(x)=\dfrac{U_0}{2}\left[1-\left(\dfrac{x}{a}\right)^2\right]^2$
(B)$U_2(x)=\dfrac{U_0}{2}\left(\dfrac{x}{a}\right)^2$
(C)$U_3(x)=\dfrac{U_0}{2}\left(\dfrac{x}{a}\right)^2\exp\left[-\left(\dfrac{x}{a}\right)^2\right]$
(D)$U_4(x)=\dfrac{U_0}{2}\left[\dfrac{x}{a}-\dfrac{1}{3}\left(\dfrac{x}{a}\right)^3\right]$
(P)The force acting on the particle is zero at $x=a$
(Q)The force acting on the particle is zero at $x=0$
(R)The force acting on the particle is zero at $x=-a$
(S)The particle experiences an attractive force towards $x=0$ in the region $|x|
(T)The particle with total energy $\dfrac{U_0}{4}$ can oscillate about the point $x=-a$
JEE (Main) 2014 Q109 Errorless 2. Work Done by Variable Force 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
A.
$aL^{2} + bL^{3}$
B.
$\frac{1}{2}(aL^{2} + bL^{3})$
C.
$\frac{aL^{2}}{2} + \frac{bL^{3}}{3}$
D.
$\frac{1}{2}\left(\frac{aL^{2}}{2} + \frac{bL^{3}}{3}\right)$
CBSE PMT 2014 Q110 Errorless 3. Conservation of Energy and Momentum 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
A.
$2mv^{2}$
B.
$4mv^{2}$
C.
$mv^{2}$
D.
$\frac{3}{2}mv^{2}$
JEE (Advanced) 2014 Q111 Errorless 3. Conservation of Energy and Momentum 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 moves from A to B, the force it applies on the wire is
A.
Always radially outwards
B.
Always radially inwards
C.
Radially outwards initially and radially inwards later
D.
Radially inwards initially and radially outwards later
JEE (Advanced) 2014 Q112 Errorless 8. Graphical Questions 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
A.
B.
C.
D.
JEE (Advanced) 2014 Q113 Errorless 9. JEE Section Numerical
Consider an elliptically shaped rail PQ in the vertical plane with OP = 3m and OQ = 4m. A block of mass 1kg is pulled along the rail from P to Q with a force of 18 N, Which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is $(n \times 10)$ joules. The value of n is (take acceleration due to gravity = 10 ms $^{-2}$ )
JEE (Advanced) 2013 Q114 Errorless 2. Work Done by Variable Force 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
A.
$\frac{2K\pi}{a}$
B.
$\frac{K\pi}{a}$
C.
$\frac{K\pi}{2a}$
D.
0
WB-JEE 2013 Q115 Errorless 4. Power MCQ
A particle is acted upon by a constant power. Then, which of the following physical quantity remains constant
A.
Speed
B.
Rate of change of acceleration
C.
Kinetic energy
D.
Rate of change of kinetic energy
JEE (Advanced) 2013 Q116 Errorless 9. JEE Section MSQ
A particle of mass $m$ is attached to one end of a mass-less spring of force constant $k$ , lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t = 0$ with an initial velocity $u_0$ . When the speed of the particle is $0.5u_0$ , it collides elastically with a rigid wall. After this collision
A.
The speed of the particle when it returns to its equilibrium position is $u_{0}$
B.
The time at which the particle passes through the equilibrium position for the first time is $t = \pi \sqrt{\frac{m}{k}}$
C.
The time at which the maximum compression of the spring occurs is $t = \frac{4\pi}{3}\sqrt{\frac{m}{k}}$
D.
The time at which the particle passes throughout the equilibrium position for the second time is $t = \frac{5\pi}{3}\sqrt{\frac{m}{k}}$
JEE (Main) 2013 Q117 Errorless 9. JEE Section MCQ
Statement-1 : A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as $f\left(\frac{1}{2}mv^{2}\right)$ then $f=\left(\frac{m}{M+m}\right)$ . Statement-2 : Maximum energy loss occurs when the particles get stuck together as a result of the collision.
A.
If both assertion and reason are true and the reason is the correct explanation of the assertion.
B.
If both assertion and reason are true but reason is not the correct explanation of the assertion.
C.
If assertion is true but reason is false.
D.
If the assertion and reason both are false.
E.
If assertion is false but reason is true.
JEE (Advanced) 2013 Q118 Errorless 9. JEE Section MCQ
A small block of mass 1 kg is released from rest at the top of a rough track. The track is a circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure below, is 150 J (Take the acceleration due to gravity, $g = 10 ms^{-2}$ ) The speed of the block when it reaches the point $Q$ is
A.
$5ms^{-1}$
B.
$10ms^{-1}$
C.
$10\sqrt{3} ms^{-1}$
D.
$20ms^{-1}$
JEE (Advanced) 2013 Q119 Errorless 9. JEE Section MCQ
A small block of mass 1 kg is released from rest at the top of a rough track. The track is a circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure below, is 150 J (Take the acceleration due to gravity, $g = 10 ms^{-2}$ ) The magnitude of the normal reaction that acts on the block at the point $Q$ is
A.
$7.5N$
B.
$8.6N$
C.
$11.5N$
D.
$22.5N$
JEE (Advanced) 2013 Q120 Errorless 9. JEE Section Numerical
A bob of mass m, suspended by a string of length $l_{1}$ , is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length $l_{2}$ , which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $\frac{l_{1}}{l_{2}}$ is
JEE (Advanced) 2013 Q121 Errorless 9. JEE Section Numerical
A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in $ms^{-1}$ ) of the particle is zero, the speed (in $ms^{-1}$ ) after 5s is
CBSE PMT (Pre.) 2012 Q122 Errorless 3. Conservation of Energy and Momentum 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
A.
Same as that of $B$
B.
Opposite to that of $B$
C.
$\theta = \tan^{-1}(1/2)$ to the $x$ -axis
D.
$\theta = \tan^{-1}(-1/2)$ to the $x$ -axis
Kerala PET 2012 Q123 Errorless 3. Conservation of Energy and Momentum 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 $(g=10ms^{-2})$
A.
$5\sqrt{2}ms^{-1}$
B.
$2\sqrt{5}ms^{-1}$
C.
$2\sqrt{3}ms^{-1}$
D.
$3\sqrt{2}ms^{-1}$
E.
$4\sqrt{2}ms^{-1}$
CBSE PMT (Mains) 2012 Q124 Errorless 3. Conservation of Energy and Momentum 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
A.
68%
B.
41%
C.
200%
D.
100%
MP PET 2012 Q125 Errorless 3. Conservation of Energy and Momentum 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
A.
0
B.
$\frac{3}{2}mv^{2}$
C.
$\frac{1}{2}mv^{2}$
D.
$2mv^{2}$