A ball of mass $m$  is dropped from a heigh $h$  on a platform fixed at the top of a vertical spring, as shown in figure. The platform is depressed by a distance $x.$  Then the spring constant is

A $300\ kg$ crate is dropped vertically onto a conveyor belt that is moving at $1.20\ m/s$ . A motor maintains the belt's constant speed. The belt initially slides under the crate, with a coefficient of friction of $0.400$ . After a short time, the crate is moving at the speed of the belt. During the period in which the crate is being accelerated, find the work done by the motor which drives the belt ………………. $\mathrm{J}$

A vertical spring with force constant $k$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

A body of mass $2\, kg$ moving with a velocity of $3\, m/sec$ collides head on with a body of mass $1\, kg$ moving in opposite direction with a velocity of $4\, m/sec$. After collision, two bodies stick together and move with a common velocity which in $m/sec$ is equal to

A body is dropped from a height $h$ . If it acquires a momentum $p$ just before striking the ground, then the mass of the body is