Figures $I, II, III$ and $IV$ depict the variation of force with time. In which of these situations is the impulse the highest?

$A$ cricket ball of mass $250\, g$ collides with a bat with velocity $10\, m/s$ and returns with the same velocity within $0.01\, s$. The force exerted on the ball is ....... $N$.

$A$ 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 $e^{-1} = 0.37$.

$A$ ball of mass $3 \ kg$ strikes a wall at an angle of $60^\circ$ with a velocity of $10 \ m/s$ and rebounds at the same angle and speed. What is the change in momentum of the ball in $MKS$ units?

$A$ body of mass $5 \,kg$ is moving with a velocity of $\vec{v}=(2 \hat{i}+6 \hat{j}) \,m/s$ at $t=0 \,s$. After time $t=2 \,s$,the velocity of the body is $(10 \hat{i}+6 \hat{j}) \,m/s$. The change in momentum of the body is ......... $kg \cdot m/s$.

$A$ player catches a cricket ball of mass $150 \, g$ moving at a speed of $20 \, m/s$. If the catching process is completed in $0.1 \, s$,the force of the blow exerted by the ball on the hands of the player is ........... $N$.