When a ball is freely fallen from a given height it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce ?

A neutron travelling with a velocity $v$ and $K.E.$ $E $ collides perfectly elastically head on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by neutron is

A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are

The diagram to the right shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?

$(I)$ $R$ and $S$ moved in the same direction after the collision.

$(II)$ Kinetic energy of the system $(R$ & $S)$ is minimum at $t = 2$ milli sec.

$(III)$ The mass of $R$ was greater than mass of $S.$

A body constrained to move along $y-$ axis is subjected to a constant force $\vec F =  - \hat i + 2\hat j + 3\hat k\,N$ The work done by this force in moving the body a distance of $4\, m$ along $y-$ axis is ............... $\mathrm{J}$

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