When a $4 \,kg$ rifle is fired,the $10 \,g$ bullet receives an acceleration of $3 \times 10^6 \,cm/s^2$. The magnitude of the force acting on the rifle (in newton) is ............

$A$ particle of mass $m$, initially at rest, is acted upon by a variable force $F$ for a brief interval of time $T$. It begins to move with a velocity $u$ after the force stops acting. The graph shows $F$ as a function of time, where the curve is a semicircle with peak force $F_0$ at time $T/2$.

$A$ ball is thrown up at an angle with the horizontal. Then,the total change of momentum by the instant it returns to the ground is

$A$ ball of mass $0.5 \ kg$ is dropped from a height of $40 \ m$. The ball hits the ground and rises to a height of $10 \ m$. The impulse imparted to the ball during its collision with the ground is (Take $g = 9.8 \ m/s^2$)

In projectile motion,two particles of masses $m_1$ and $m_2$ have velocities $\vec{V}_1$ and $\vec{V}_2$ respectively at time $t=0$. Their velocities become $\vec{V}_1^{\prime}$ and $\vec{V}_2^{\prime}$ at time $2t$ while still moving in air. The value of $[(m_1 \vec{V}_1^{\prime} + m_2 \vec{V}_2^{\prime}) - (m_1 \vec{V}_1 + m_2 \vec{V}_2)]$ is ($g =$ acceleration due to gravity).

$A$ particle of mass $m$ strikes elastically on a wall with velocity $v$,at an angle of $60^{\circ}$ from the wall. The magnitude of the change in momentum of the particle along the wall is: