$A$ $10 \,g$ bullet moving at $200 \,m/s$ stops after penetrating $5 \,cm$ of a wooden plank. The average force exerted on the bullet will be .......... $N$.

$A$ spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released,the spring exerts an equal and opposite force on each cart for the same time $t$. If the coefficient of friction $\mu$ between the ground and the carts is the same,find the ratio of the displacements of the two toy carts.

$A$ mass of $1 \text{ kg}$ is kept on an inclined plane with $30^\circ$ inclination with respect to the horizontal plane and it is at rest initially. Then,the whole assembly is moved up with a constant velocity of $4 \text{ m/s}$. The work done by the frictional force in time $2 \text{ s}$ is . . . . . . $\text{J}$. (Take $g = 10 \text{ m/s}^2$)

$A$ horizontal force $F = mg/3$ is applied on the upper surface of a uniform cube of mass $m$ and side $a$,which is resting on a rough horizontal surface having $\mu_S = 1/2$. The distance between the lines of action of $mg$ and the normal reaction $N$ is:

$A$ balloon of mass $M$ is descending at a constant acceleration $\alpha$. When a mass $m$ is released from the balloon,it starts rising with the same acceleration $\alpha$. Assuming that its volume does not change,what is the value of $m$?

The graph below shows the variation of a force $F$ with time $t$ on a body which is moving in a straight line. The dependence of force on time is $F \propto t^{n}$. Initially,the body is at rest. If the speed of the object is $2 \, m/s$ at $3 \, s$,then the speed at $4 \, s$ will be approximately (in $m/s$):