A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block 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 ................... $\mathrm{J}$

In one dimensional case, the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ............ $\mathrm{ergs}$

A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be

A body constrained to move along $y-$ axis is subjected to a constant force $\vec F =  - \hat i + 2\hat j + 3\hat k\,N$ The work done by this force in moving the body a distance of $4\, m$ along $y-$ axis is ............... $\mathrm{J}$

A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be