A thin uniform bar lies on a frictionless horizontal surface and is free to move in any way on the surface. Its mass is $0.300\, kg$ and length is $2 \,m$ . Two particles each of mass $0.100\, kg$ are moving on the same surface and towards the two ends of the bar in the direction perpendicular to the bar such that one with velocity $10\, m/s$ towards one end and the other with velocity $5\, m/s$ towards the other end. If collision between particles and bar is completely elastic and both particles strike with the bar simultaneously. The velocity of centre of mass of the bar after the collision is ...... $m/s$

An inelastic ball is dropped from a height of $100\, m$. Due to earth$20\%$ of its energy is lost. To what height the ball will rise ......... $m$

Two particles $A$ and $B,$ move with constant  velocities $\vec v_1$ and $\vec v_2$. At the initial moment their position vectors are $\vec r_1$ and $\vec r_2$ respectively. The condition for particles $A$ and $B$ for their collision is

A proton of mass $m$ collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of $90^o$ with respect to each other. The mass of unknown particle is

Two massless string of length $5\, m$ hang from the ceiling very near to each other as shown in the figure. Two balls $A$ and $B$ of masses $0.25 \,kg$ and $0.5 \,kg$ are attached to the string. The ball $A$ is released from rest at $a$ height $0.45\, m$ as shown in the figure. The collision between two balls is completely elastic. Immediately after the collision, the kinetic energy of ball $B$ is $1\, J$. The velocity of ball $A$ just after the collision is

A body of mass $5\, kg$ moving with a velocity $10\,m/s$ collides with another body of the mass $20 \,kg$ at, rest and comes to rest. The velocity of the second body due to collision is ......... $m/s$