When the momentum of a body increases by $100\%$, its $KE$ increases by ………….. $\%$

A sphere of mass $0.1\,\,kg$  is attached to a cord of $1\,m$ length. Starting from the height of its point of suspension this sphere hits a block of same mass at rest on a frictionless table. If the impact is elastic, then the kinetic energy of the block after the collision is …………. $\mathrm{J}$

A block of mass $0.50\, kg$ is moving with a speed of $2.00\, ms^{-1}$ on a smooth surface. It strikes another mass of $1.00\, kg$ and then they move together as a single body. The energy loss during the collision is ………….. $\mathrm{J}$

Force acting on a particle moving in a straight line varies with the velocity of the particle as $F = \frac{K}{\upsilon }$  where $K$ is a constant. The work done by this force in time $t$ is

A 3.628 kg freight car moving along a horizontal rail road spur track at $7.2\; km/hour$ strikes a bumper whose coil springs experiences a maximum compression of $30 \;cm$ in stopping the car. The elastic potential energy of the springs at the instant when they are compressed $15\; cm$ is [2013]

(a) $12.1 \times 10^4\;J$ (b) $121  \times 10^4\;J$ (c) $1.21 \times 10^4\;J$ (d) $1.21  \times 10^4\;J$