A ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending  down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $\mathrm{m}/ \mathrm{s}$

A uniform chain of length $2\, m$ is kept on a table such that a length of $60\, cm$ hangs freely from the edge of the table. The total mass of the chain is $4\, kg$. What is the work done in pulling the entire chain on the table ? ................ $\mathrm{J}$

If the kinetic energy of a body is directly proportional to time $t$, the magnitude of force acting on the body is 
$(i)$ directly proportional to $\sqrt t$
$(ii)$ inversely proportional to $\sqrt t$
$(iii)$ directly proportional to the speed of the body
$(iv)$ inversely proportional to the speed of body

A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............

A particle of mass $m$ strikes the ground inelastically, with coefficient of restitution $e$

The kinetic energy $K$ of a particle moving along a circle of radius $R$ depends upon the distance $s$ as $K = as^2$. The force acting on the particle is