Two masses of $1 \,gm$ and $4 \,gm$ are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

A force of $5\,N$ acts on a body of mass $5\, kg$ for $1\, second$ and gives it a momentum $p$ and kinetic energy $E$. If the same force accelerates the same body through $1\,m$, the momentum and energy attained by the body are $p’$ and $E’$ respectively. Which of the following relations is correct?

If the kinetic energy of a body is directly proportional to time $t,$ the magnitude of force acting on the body is

$(i)$ directly proportional to $\sqrt t$
$(ii)$  inversely proportional to  $\sqrt t$
$(iii)$ directly proportional to the speed of the body
$(iv)$ inversely proportional to the speed of body

A stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $V_B$ respectively. The ratio of their kinetic energies $\left(\mathrm{K}_B: \mathrm{K}_{\mathrm{A}}\right)$ is :

A bullet is fired from a rifle. If the rifle recoils freely, then the kinetic energy of the rifle is