$A$ body of mass $3 \, kg$ hits a wall at an angle of $60^\circ$ with the wall and returns at the same angle. The speed of the body is $10 \, m/s$ and the impact time is $0.2 \, s$. Calculate the force exerted on the wall.

$A$ sphere is placed rotating with its centre initially at rest in a corner as shown in figures $(a)$ and $(b)$. The coefficient of friction between all surfaces and the sphere is $\mu = \frac{1}{3}$. Find the ratio of the frictional force $\frac{f_a}{f_b}$ exerted by the ground in situations $(a)$ and $(b)$.

As shown in the figure,a block of mass $2 \ kg$ is placed on a rough inclined plane such that it just touches the spring. The block moves downwards. What will be the maximum compression of the spring in $cm$?

$A$ wooden block of mass $2\; kg$ rests on a soft horizontal floor. When an iron cylinder of mass $25\; kg$ is placed on top of the block,the floor yields steadily and the block and the cylinder together go down with an acceleration of $0.1\; m/s^2$. What is the action of the block on the floor $(a)$ before and $(b)$ after the floor yields? Take $g = 10\; m/s^2$. Identify the action-reaction pairs in the problem.

State whether the following statements are true or false:
$(a)$ $A$ necessary condition for equilibrium is that the acceleration must be zero.
$(b)$ Centripetal force is always in the opposite direction of centrifugal force.
$(c)$ $A$ man is at rest on a perfectly smooth ice surface in the middle of a pond. He can reach the shore by using Newton's first law.
$(d)$ An object is in equilibrium only if it is at rest.

Which one of the following is not used to reduce friction?