$A$ ball of mass $150\,g$ starts moving with an acceleration of $20\,m/s^2$. When hit by a force,which acts on it for $0.1\,s$. The impulsive force is ........ $N-s$.

If impulse $I$ varies with time $t$ as $I \text{ (kg m s}^{-1}) = 20 t^2 - 40 t$. The change in momentum is minimum at ........... $s$.

$A$ solid horizontal surface is covered with a thin layer of oil. $A$ rectangular block of mass $m = 0.4 \ kg$ is at rest on this surface. An impulse of $1.0 \ N \ s$ is applied to the block at time $t = 0$ so that it starts moving along the $x$-axis with a velocity $v(t) = v_0 e^{-t/\tau}$,where $v_0$ is a constant and $\tau = 4 \ s$. The displacement of the block,in metres,at $t = \tau$ is. . . . . . . Take $e^{-1} = 0.37$.

$A$ ping-pong ball of mass $m$ is floating in air by a jet of water emerging out of a nozzle. If the water strikes the ping-pong ball with a speed $v$ and just after collision the water falls dead,the rate of flow (in $kg/s$) of water in the nozzle is equal to

$A$ machine gun can fire $200$ bullets $\min^{-1}$. If $35 \ g$ bullets are fired at a speed of $750 \ m \ s^{-1}$, the average force exerted by the gun on the bullets is, (in $N$)

Two objects of different masses have the same momentum. Which of the two objects will be moving faster?