Work-energy-power practice · Mixed difficulty

A particle moves in a circle of radius 5 cm with constant speed and time period $0.2\,\,\pi$ seconds. The acceleration of the particle is [in $m/{s^2}$]

A particle of mass 2 kg starts moving in a straight line with an initial velocity of $2\mathrm{\;m}{\mathrm{s}^{ - 1}}$ at a constant acceleration of $2\mathrm{\;m}{\mathrm{s}^{ - 2}}$. Then rate of change of kinetic energy

A machine gun mounted on a 2000 kg car on a horizontal frictionless surface fires 10 bullets per second. If 10 g be the mass of each bullet and 500 $\mathrm{m}{\mathrm{s}^{ - 1}}$, the velocity of each bullet, then the acceleration of the car will be

A water pump lifts water at the rate of 5 litre per second through an average height of $8 \mathrm{~m}$ from a well of depth $12 \mathrm{~m}$. Its power will be:

A certain body of mass $M$ moves under the action of a conservative force with potential energy $U$ given by $U=\frac{K x}{x^2+a^2}(x \rightarrow$ distance, $a \rightarrow$ amplitude$)$ In this equation the units of ${K}$ will be equal to that of:

A ball falls from a height of $16 {~m}$ on a floor and rebounds to a height of $4 {~m}$. The coefficient of restitution for collision is :-

A uniform force of $\left( {3\hat i + \hat j} \right)$ newton acts on a particle of mass 2 kg. The particle is displaced from position $\left( {2\hat i + \hat k} \right)m$ to position $\left( {4\hat i + 3\hat j - \hat k} \right)m$. The work done by the force on the particle is

Two blocks of masses ${m_1}\,and\,{m_2}$ are connected by a massless spring and placed at smooth surface. The spring initially stretched and released. Then

An iron nail is dropped from a height h from the level of a sand bed. If it penetrates through a distance x in the sand before coming to rest, then average force exerted by the sand on nail is

A force of $10\hat i - 3\hat j + 6\hat k$ N acts on a body of mass 100 g and displaces it from $6\hat i + 5\hat j - 3\hat k$ m to $10\hat i - 2\hat j + 7\hat k$ m. The work done is

Statement-1: A block of mass ' $M$ ' is placed on a moving railroad car moving with velocity ' $v$ '. The kinetic energy of the block is $\frac{1}{2} M v^2$ in all frames.

Statement-2: The kinetic energy of a system or body is different in different frames.

Two springs A and B are identical but A is harder than $B({k_A} > {k_B})$. Let ${W_A}\,and\,{W_B}$ represent the work done when the springs are stretched through the same distance and ${W'_A}\,and\,{W'_B}$ are the work done when these are stretched by equal forces, then which of the following is true

The string of a pendulum of length l is displaced through ${90^0}$ from the vertical and released. Then the minimum strength of the string in order to withstand the tension as the pendulum passes through the mean position is

One kilowatt hour is a unit of:

One man takes 1 minute to raise a box to a height of 1 m and another man takes $\frac{1}{2}$ minute to do so. The energy of the two is

A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break

A rope ladder with a length $l$ carrying a man with a mass m at its end is attached to the basket of balloon with a mass M. The entire system is in equilibrium in the air. As the man climbs up the ladder into the balloon, the balloon descends by a height h. Then the potential energy of the man