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

$A$ machine gun fires a bullet of mass $65 \, g$ with a velocity of $1300 \, m/s$. The man holding it can exert a maximum force of $169 \, N$ on the gun. The number of bullets he can fire per second will be ............

In a force $F$ versus time $t$ graph for an object,the area enclosed in a time interval of $1 \ s$ is $100 \ Ns$. Calculate the magnitude of the force. (in $N$)

$A$ batsman hits a ball of mass $0.2 \ kg$ straight towards the bowler without changing its initial speed of $6 \ m/s$. What is the impulse imparted to the ball (in $Ns$)?

$A$ particle moves in the $x-y$ plane under the action of a force $\overrightarrow{F}$ such that the value of its linear momentum $\overrightarrow{P}$ at any time $t$ is $P_x = 2\cos t$ and $P_y = 2\sin t$. The angle $\theta$ between $\overrightarrow{F}$ and $\overrightarrow{P}$ at a given time $t$ will be $\theta = $ ........... $^o$.

$A$ body of $2\, kg$ has an initial speed of $5\, ms^{-1}$. $A$ force acts on it for some time in the direction of motion. The force-time graph is shown in the figure. Find the final speed of the body in $ms^{-1}$.