A particle of mass $500 \,gm$ is moving in a straight line with velocity $v=b x^{5 / 2}$. The work done by the net force during its displacement from $x=0$ to $x =4 \,m$ is ...................$J$ (Take $b =0.25 \,m ^{-3 / 2} s ^{-1}$ )

A person draws water from a $5\,m$ deep well in a bucket of mass $2\,kg$ of capacity $8\,litre$ by a rope of mass $1\,kg.$ What is the total work done by the person ? .............. $\mathrm{J}$ (Assume $g = 10\,m/sec^2$ )

An engine is attached to a wagon through a shock absorber of length $1.5\, {m}$. The system with a total mass of $40,000\, {kg}$ is moving with a speed of $72\, {kmh}^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0\, {m}$. If $90\, \%$ of energy of the wagon is lost due to friction, the spring constant is $....\, \times 10^{5}\, {N} / {m}$

Figure here shows the frictional force versus displacement for a particle in motion. The loss of kinetic energy in travelling over $s = 0$ to $20\, m$ will be......$J$

A uniform chain of mass $m$ and length $L$ is originally placed mid-way on the top of a fixed smooth double-sided wedge (Figure- $A$). The length of each side of the wedge is $L$ . It is then given a slight push. The kinetic energy of the chain when the whole chain has just slid to the left side of the wedge (Figure- $B$), is :

A $2\ kg$ object is floating at rest, acted upon by only force as indicated in figure. Find the total work done by the force in $3\ sec$ ..................... $\mathrm{J}$