Work-energy-power practice · Mixed difficulty

Two students are sitting face to face, at two ends of a long compartment of a train, running at a constant acceleration. They toss a ball to each other, with the same muzzle velocity and at the same inclination to the vertical.
Statement-1: The time intervals for the free fall in either direction are equal.
Statement-2: In the frame of compartment velocity is changing but the vertical velocity remains unaffected by the horizontal acceleration of the cart.

A particle is released from a height H. At certain height its kinetic energy is two times its potential energy. Height and speed of particle at that instant are

The slope of the kinetic energy displacement curve of a particle in motion is

A particle moves with constant angular velocity in circular path of certain radius and is acted upon by a certain centripetal force F. If the angular velocity is doubled keeping radius the same, the new force will be

Force of 4 N is applied on a body of mass 20 kg. The work done in 3rd second is

Which of the following is not a perfectly inelastic collision

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ${a_c}$  is varying with time as ${a_c} = {k^2}r{t^4},$, where k is a constant. The power delivered to the particle by the forces acting on its is

The mass of ship is $2 \times {10^7}\;kg$. On applying a force of $25 \times {10^5}\;N$ , it is displaced through 25 m. After the displacement, the velocity acquired by the ship will be

The kinetic energy of a body is $K$. If one – fourth of its mass is removed and velocity is doubled, its new kinetic energy is,

A bus of mass 6 metric tons is pulled at a speed of 18 kmpH on a smooth incline of inclination 1in 20. Power of the engine is $\left[ {g = 10\,m{s^{ - 2}}} \right]$

A particle experiences a variable force $\vec{F}=\left(2 x^2 \hat{i}+2 y \hat{j}\right) N$ in a horizontal $X-Y$ plane. where $x$ and $y$ are in meters. If the particle moves from point $(0,1)$ to point $(1,2)$ in the $X-Y$ plane, then kinetic energy charges by

The potential energy $U=3 a x^3-2 b x^2$. The force constant is represented by

A bucket filled with water is tied to a rope of length 0.5 m and is rotated in a circular path in vertical plane. The least velocity it should have at the lowest point of circle so that water dose not spill is $\left( {g = 10\;\mathrm{m}{\mathrm{s}^{ - 2}}} \right)$

In a conservative field, if the potential energy $U$ as a function of position $x$ is given as $U=x^3+2 x+3,$ then the corresponding conservative force is given by:

A can filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. The time period of  revaluation will be

Assertion: A truck and a car moving with the same kinetic energy are brought to rest by the application of breaks which provide equal retarding forces. Both come to rest in equal distance.
Reason: It is possible that the speed of a body is zero but velocity is not zero.

Which of the following statements is wrong?

A body of mass m starts moving from rest along x-axis so that its velocity varies as $v = a\sqrt s$ where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t second after the start of the motion is:

A body of mass $1 \mathrm{~kg}$ is rotated in a horizontal circle of radius $1 \mathrm{~m}$ and moves with velocity $2 \mathrm{~m} / \mathrm{sec}$. The work done in 10 revolutions is

A circular road of radius 1000 m has banking angle ${45^0}$. The maximum safe speed of a car having mass 2000 kg will be, if the coefficient of friction between tyre and road is 0.5

A body of mass $8 \mathrm{~kg}$ and another of mass $2 \mathrm{~kg}$ are moving with equal kinetic energy. The ratio of their respective momenta will be

A bomb of mass 10 kg explodes into two pieces of mass 5 kg and 5 kg. The velocity of mass 5 kg is 16 m/s. The K.E of mass 5 kg is

Statement-I: A quick collision between two bodies is more violent than slow collision, even when initial and final velocities are identical.
Statement-II: The rate of change of momentum determines that the force is small or large.

In which of the following cases, can the work done increase the potential energy?

Power supplied to a particle of mass 2 kg varies with time as $P = \frac{{3{t^2}}}{2}$ watt. Here t is in second. If the velocity of particle at t=0 is v=0, the velocity of particle at time t=2 s will be

Two masses of 1 kg and 4 kg are moving with equal kinetic energy. The ratio of their linear momentum is

Motion of a particle in $x - y$ plane is described by a set of following equations $x = 4\sin \left( {\frac{\pi }{2} - \omega t} \right)m$ and $y = 4\sin \left( {\omega t} \right)m.$ The path of the particle will be

This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. If two springs $S_1$ and $S_2$ of the force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.
Statement-I: If stretched by the same amount, work done on $S_1$, will be more than that of $S_2$
Statement-II : $k_1 < k_2$

A particle is moving along a circular path with a uniform speed. How does its angular velocity change when it completes half of the circular path?

Two bodies of masses $4 \mathrm{~kg}$ and $5 \mathrm{~kg}$ are moving with equal momentum. Then the ratio of their respective kinetic energies is