$A$ gun applies a force $F$ on a bullet which is given by $F = (100 - 0.5 \times 10^{5} t) \ N$. The bullet emerges out with a speed of $400 \ m/s$. Find the impulse exerted until the force on the bullet becomes zero (in $N \cdot s$).

$A$ small mass $m$ is launched from the top of a cliff with speed $V$ at an angle of $30^{\circ}$ above the horizontal. When the mass reaches the ground,its velocity is directed at $45^{\circ}$ below the horizontal. Which one of the following choices is the magnitude of the total impulse that was imparted to the mass during its flight? Ignore air resistance.

$A$ particle moves in the $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{P}(t) = \hat{i} \cos(kt) - \hat{j} \sin(kt)$. If $k$ is a constant,the angle between $\vec{F}$ and $\vec{P}$ will be:

$A$ 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

$A$ stream of glass beads, each with a mass of $15 \ g$, comes out of a horizontal tube at a rate of $100 \ \text{beads per second}$. The beads fall a distance of $5 \ m$ to a balance pan and bounce back to their original height. How much mass (in $kg$) must be placed in the other pan of the balance to keep the pointer at zero?

$A$ body of mass $5 \, kg$ is moving with a momentum of $10 \, kg \cdot m/s$. $A$ force of $0.2 \, N$ acts on it in the direction of motion of the body for $10 \, seconds$. The increase in its kinetic energy is ............... $J$.