A body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x\,\,cm$ into the sand, the average resistance offered by the sand of the body is
$Mg\left( {\frac{h}{x}} \right)$
$Mg\left( {1\,+\,\frac{h}{x}} \right)$
$Mgh\,+\,Mgx$
$Mg\left( {1\,-\,\frac{h}{x}} \right)$
Figure shows the vertical section of frictionless surface. $A$ block of mass $2\, kg$ is released from the position $A$ ; its $KE$ as it reaches the position $C$ is ................ $\mathrm{J}$
A mass $m$ moving horizontally with velocity $v_0$ strikes a pendulum of mass $m$. If the two masses stick together after the collision, then the maximum height reached by the pendulum is
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 ............. $\mathrm{J}$
Power applied to a particle varies with time as $P = [3t^2 -2t + 1]$ $watt$ then the change in kinetic energy of particle from $t = 2\,sec$ to $t = 4\,sec.$ ............... $\mathrm{J}$
The spacecraft of mass $M$ moves with velocity $V$ in free space at first, then it explodes breaking into two pieces. If after explosion a piece of mass $m$ comes to rest, the other piece of space craft will have a velocity