Work-energy-power practice · Medium

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

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 $\left( {g = 10\;\mathrm{m}{\mathrm{s}^{ - 2}}} \right)$

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

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

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?

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

A sphere collides with another sphere of identical mass. After collision, the two spheres move. The collision is inelastic. Then the angle between the directions of the two spheres is

Assertion: No work is done by a force on an object when the point of application of the force does not move.
Reason: A small block of mass $m$ is kept on a rough inclined surface of inclination $a$ fixed in an elevator. The elevator goes up with a uniform velocity $u$ and the block does not slide on the wedge. Then the work done by the force of friction on the block in time $t$ will be $mgut \sin ^2 \alpha$.

Statement I A cyclist is moving on an unbanked road with a speed of $7\,km{h^{ - 1}}$ and takes a sharp circular turn along a path of radius of 2 m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve $\left( {g\, = \,9.8\,m/{s^2}} \right)$
Statement II If the road is banked at an angle of ${45^\mathrm{o}}$, cyclist can cross the curve of 2 m radius with the speed of $18.5\,km{h^{ - 1}}$ without slipping.
In the light of the above statements, choose the correct answer from the options given below.

Which of the following is not a conservative force

The potential energy of a body (U) of mass 1 kg varies with position co-ordinates of the particle x (m) and y (m) as $U = \mathrm{ }4x + \mathrm{ }3y$. The acceleration of the particle is

In which case does the potential energy decrease

The area under the displacement-force curve gives

If KE of the particle of mass m performing UCM in a circle of radius r is E. Find the acceleration of the particle

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