A projectile of mass $3m$ is moving at $40\, m/s$ at is highest point, where it breaks into two parts $m$ and $2m$. Mass $2m$ moves vertically up at $25\, m/s$. The other part will move at speed  .................... $\mathrm{m}/ \mathrm{s}$

A particle of mass $m$ with an initial velocity $u\hat i$ collides perfectly elastically with a mass $3m$ at rest. It moves with a velocity $v\hat j$ after collision, then, $v$ is given by

A body of mass $2\,kg$ makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body? ................ $ \mathrm{kg}$

A ball of mass $m$ moving with velocity $v$ collides head-on with the second ball of mass $m$ at rest. If the coefficient of restitution is $e$ and velocity of first ball after collision is $v_1$ and velocity of second ball after collision is $v_2$ then

A big ball of mass $M$, moving with velocity $u$ strikes a small ball of mass $m$, which is at rest. Finally small ball obtains velocity $u$ and big ball $v$. Then what is the value of $v$

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- ................ $\mathrm{m}/ \mathrm{s}$