A ball is released from a height of $10\, m$. If after the impact there is loss of $40\%$ in its  energy, the ball shall rise upto- ................. $\mathrm{m}$

Consider the collision depicted in Figure to be between two billiard balls with equal masses $m_{1}=m_{2}$ The first ball is called the cue while the second ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle $\theta_{2}=37^{\circ} .$ Assume that the collision is elastic and that friction and rotational motion are not important. Obtain $\theta_{1}$

How much energy produced in burning of $1\, kg$ coal ?

A force acts on a $3 \,gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4{t^2} + {t^3}$, where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \,seconds$ is ..... $mJ$

From a building two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ downwards (both vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground, then

A block of mass ' $m$ ' (as shown in figure) moving with kinetic energy $E$ compresses a spring through a distance $25\,cm$ when, its speed is halved. The value of spring constant of used spring will be $nE\; Nm ^{-1}$ for $n=$