A bullet of mass $5 \,g$ is shot from a gun of mass $5 \,kg$. The muzzle velocity of the bullet is $500\, m/s$. The recoil velocity of the gun is ........... $m/s$
$0.5$
$0.25$
$1$
Data is insufficient
A simple pendulum of length $1 \mathrm{~m}$ has a wooden bob of mass $1 \mathrm{~kg}$. It is struck by a bullet of mass $10^{-2} \mathrm{~kg}$ moving with a speed of $2 \times 10^2 \mathrm{~ms}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
A rifle man, who together with his rifle has a mass of $100\,kg$, stands on a smooth surface and fires $10$ shots horizontally. Each bullet has a mass $10\,g$ and a muzzle velocity of $800\,ms ^{-1}$. The velocity which the rifle man attains after firing $10$ shots is $..........\,ms^{-1}$
The motion of a rocket is based on the principle of conservation of
A man (mass $= 50\, kg$) and his son (mass $= 20\, kg$) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70\, ms^{-1}$ with respect to the man. The speed of the man with respect to the surface is ........ $ms^{-1}$
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: