A gun fires a bullet of mass $50 \,gm$ with a velocity of $30\,m\,{\sec ^{ - 1}}$. Because of this the gun is pushed back with a velocity of $1\,m\,{\sec ^{ - 1}}$. The mass of the gun is .......... $kg$

A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \,ms ^{-1}$ and $40 \,ms ^{-1}$ respectively. The velocity of the third piece will be ............... $\,ms ^{-1}$

A $^{238}U$ nucleus decays by emitting an $\alpha$ particle of speed $v\,m{s^{ - 1}}$. The recoil velocity of the residual nucleus is (in $m{s^{ - 1}}$)

A shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/3$ remains stationary. The velocity of other part will be

A bomb is projected with $200\,m/s$ at an angle $60^o$ with horizontal. At the highest  point, it explodes into three particles of equal masses. One goes vertically upward with  velocity $100\,m/sec$, second particle goes vertically downward with the same velocity as  the first. Then what is the velocity of the third one-

A projectile is fired with velocity $u$ at an angle $\theta$ with horizontal. At the highest point of its trajectory it splits up into three segments of masses $m, m$ and $2 \,m$. First part falls vertically downward with zero initial velocity and second part returns via same path to the point of projection. The velocity of third part of mass $2 \,m$ just after explosion will be