A steel ball of radius $2\, cm$ is at rest on a frictionless surface. Another ball of radius $4\,cm$ moving at a velocity of $81 \,cm/sec$ collides elastically with first ball. After collision the smaller ball moves with speed of ............. $\mathrm{cm} / \mathrm{sec}$

A train is moving at a constant speed $V$. When its driver observes another train in front of him on the same track and moving in the same direction with constant speed $u$. If the distance between the trains be $x$, then what should be the minimum retardation of the train so as to avoid collision?

Two bodies $A$ and $B$ collide as shown in Fig. $(i)$ and $(ii)$ Which statement is true ?

A particle of mass $m$ is moving along the $x$ -axis with initial velocity $u \hat i$. It collides elastically with a particle of mass $10\, m$ at rest and then moves with half its initial kinetic energy (see figure). If $\sin \theta_{1}=\sqrt{n} \sin \theta_{2}$ then value of $n$ is.....

A bullet of mass $0.01\, kg$ and travelling at a speed of $500 \,m/s$. strikes a block of  mass $2 \,kg$. which is suspended by a string of length $5\,m$. The centre of gravity of the  block is found to raise a vertical distance of $0.1\,m$. What is the speed of the bullet  after it emerges from the block- ................ $\mathrm{m}/ \mathrm{s}$

A particle of mass $m$ collides with a heavy mass (at rest) elastically and after collision returns with $4/9$ of it's initial kinetic energy. The mass of heavy object is ............... $\mathrm{m}$