A body is falling under gravity from rest. When it loses a gravitational potential energy by $U,$ its speed increases to $v.$ The mass of the body shall be

An object has momentum $p$ & kinetic energy $E$. If its momentum becomes $2\,p$ then  its kinetic energy will be :-

The bob of a pendulum of length $l$ is pulled aside from its equilibrium position through an angle $\theta $ and then released. The bob will then pass through its equilibrium position with speed $v$ , where $v$ equals

The potential energy of a long spring when stretched by $2\, cm$ is $U.$ If the spring is stretched by $8\, cm$ the potential energy stored in it is

$A$ ball is projected from ground with a velocity $V$ at an angle $\theta$ to the vertical. On its path it makes an elastic collison with $a$ vertical wall and returns to ground. The total time of flight of the ball is 

State if each of the following statements is true or false. Give reasons for your answer.

$(a)$ In an elastic collision of two bodies, the momentum and energy of each body is conserved.

$(b)$ Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

$(c)$ Work done in the motion of a body over a closed loop is zero for every force in nature.

$(d)$ In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.