Consider an elliptically shaped rail $PQ$ in the vertical plane with $OP=3 \mathrm{m}$ and $OQ=4 \mathrm{m}$. A block of mass $1 \mathrm{kg}$ is pulled along the rail from $P$ to $Q$ with a force of $18 \mathrm{N}$, which is always parallel to line $PQ$ (see Fig.). Assuming no frictional losses, the kinetic energy of the block when it reaches $Q$ is $\left(\mathrm{n}\times 10\right) \mathrm{J}$ Joules. Find the value of $n$ (take acceleration due to gravity$=10 \mathrm{m}/{\mathrm{s}}^2$).

 

A light Inextensible string that goes over a smooth fixed pulley as shown In Fig. connects two blocks of masses $0.36 \mathrm{kg}$ and $0.72 \mathrm{kg}$. Taking $g=10 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$, find the work done (in Joule) by string on the block of mass $0.36 \mathrm{kg}$ during the first second after the system is released from rest.

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a$ is varying with time $t$ as $a_c=k^{2}r{t}^2$ where $k$ is a constant. The power delivered to the particle by the force acting on it is