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:

A body of mass $5 \,kg$  explodes at rest into three fragments with masses in the ratio $1 : 1 : 3$. The fragments with equal masses fly in mutually perpendicular directions with speeds of $21 \,m/s$. The velocity of the heaviest fragment will be

A man is standing at the centre of frictionless pond of ice. How can he get himself to the shore

An object of mass $2 \,kg$ at rest at origin starts moving under the action of a force $\vec{F}=\left(3 t^2 \hat{i}+4 \hat{j}\right) N$ The velocity of the object at $t=2 \,s$ will be ............. $m / s$

Two skaters $A$ and $B$ of weights in the ratio $5 : 7$ start facing each other $6\,metres$ apart on a horizontal smooth surface. They pull on a rope stretched between them. How far has each moved when they meet?

A hemisphere of radius $R$ and of mass $4m$ is free to slide with its base on a smooth horizontal table. A particle of mass $m$ is placed on the top of the hemisphere. The angular velocity of the particle relative to hemisphere at an angular displacement $\theta $ when velocity of hemisphere $v$ is