A body of mass $m_1$ moving with an unknown velocity of $v_1 \hat i$ undergoes a collinear collision with a body of mass $m_2$ moving with a velocity $v_2 \hat i$ . After collision $m_1$ and $m_2$ move with velocities of $v_3 \hat i$ and $v_4 \hat i$ respectively. If $m_2 = 0.5\, m_1$ and $v_3 = 0.5\, v_1$ then $v_1$ is:

An artillery piece of mass $M_1$ fires a shell of mass $\mathrm{M}_2$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:

An initially stationary device lying on a frictionless floor explodes into two pieces and slides across the floor one piece is moving in positive $x$ direction then other peice is moving in

If final momentum is equal to initial momentum of the system then

A $6 \,kg$ bomb at rest explodes into three equal pieces $P, Q$ and $R$. If $P$ flies with speed $30 \,m / s$ and $Q$ with speed $40 \,m / s$ making an angle $90^{\circ}$ with the direction of $P$. The angle between the direction of motion of $P$ and $R$ is about

A body is moving with a velocity $v$, breaks up into two equal parts. One of the part retraces back with velocity $v$. Then the velocity of the other part is