A particle of mass $m$ is moving with speed $2\, v$ collides with a mass $2\,m$ moving with speed $v$ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass $m$, which move at angle $45^o$ with respect to the original direction. The speed of each of the moving particle will be

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 ......... $m$

A ball of mass $2\,m$ is moving with velocity $v$ on a smooth surface collides elastically headon with another ball of mass $m$. If ball of mass $m$ reaches upto top of frictionless elevated plane, then velocity $v$ of heavy ball must be

An alpha-particle of mass $m$ suffers $1-$ dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, $64\%$ of its initial kinetic energy. The mass of the nucleus is .......... $\mathrm{m}$

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 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