$A$ mass of $1 \ kg$ is suspended by a string $A$. Another string $C$ is connected to its lower end (see figure). If a sudden jerk is given to $C$,then

$A$ cricket ball of mass $0.25 \,kg$ with speed $10 \,m/s$ collides with a bat and returns with the same speed within $0.01 \,s$. The force exerted on the bat is: (in $\,N$)

$A$ particle of mass $m$ moving with velocity $(3\hat{i} + 2\hat{j}) \ m/s$ collides with another body of mass $M$ and finally moves with velocity $(-2\hat{i} + \hat{j}) \ m/s$. Then during the collision:

$A$ 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 ........... $N$.

Two billiard balls of equal mass $30 \, g$ strike a rigid wall with the same speed of $108 \, km/h$ (as shown) but at different angles. If the balls get reflected with the same speed, then the ratio of the magnitude of impulses imparted to ball $'a'$ and ball $'b'$ by the wall along the $'X'$ direction is:

The position-time $(x-t)$ graph of a moving body of mass $2 \, kg$ is shown in the figure. The impulse on the body at $t=4 \, s$ is