$A$ ball is dropped from a height of $20 \, cm$. The ball rebounds to a height of $10 \, cm$. What is the percentage loss of energy? ................ $\%$

The position $x$ of a particle moving along the $x$-axis at time $t$ is given by the equation $t = \sqrt{x} + 2$,where $x$ is in metres and $t$ is in seconds. The work done by the force in the first $4 \ s$ is .............. $J$.

$A$ block of mass '$m$' with an initial kinetic energy '$E$' moves up an inclined plane of inclination '$\theta$'. If '$\mu$' is the coefficient of friction between the plane and the body,the work done against friction before coming to rest is

$A$ $0.5\, kg$ ball is thrown up with an initial speed $14\, m/s$ and reaches a maximum height of $8.0\, m$. How much energy is dissipated by air drag acting on the ball during the ascent? (Take $g = 9.8\, m/s^2$)

An open knife edge of mass $m$ is dropped from a height $h$ on a wooden floor. If the blade penetrates up to the depth $d$ into the wood,the average resistance offered by the wood to the knife edge is

Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially,$S_1$ is at rest and $S_2$ is moving with velocity $v$ along the $x$-axis. After the collision,$S_2$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The sphere $S_1$ moves after the collision: