$A$ $0.5\, kg$ ball moving with a speed of $12\, m/s$ strikes a hard wall at an angle of $30^\circ$ with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for $0.25\, s$,the average force acting on the wall is ........... $N$.

$A$ long plank $P$ of mass $5\, kg$ is placed on a smooth floor. On $P$ is placed a block $Q$ of mass $2\, kg$. The coefficient of friction between $P$ and $Q$ is $0.5$. If a horizontal force $15\, N$ is applied to $Q$,as shown,and you may take $g$ as $10\, N/kg$,then which of the following statements is correct?

$A$ force of $mg$ is applied to block $B$ to keep the system in equilibrium. Find the value of $T_1$.

$A$ helicopter of mass $2000 \,kg$ rises with a vertical acceleration of $15 \,m s^{-2}$. The total mass of the crew and passengers is $500 \,kg$. Calculate the magnitude and direction of the following (take $g = 10 \,m s^{-2}$):
$(a)$ Force on the floor of the helicopter by the crew and passengers.
$(b)$ Action of the rotor of the helicopter on the surrounding air.
$(c)$ Force on the helicopter due to the surrounding air.

The masses of blocks $A$ and $B$ are $m$ and $M$ respectively. Between $A$ and $B$,there is a constant frictional force $F$ and $B$ can slide on a smooth horizontal surface. $A$ is set in motion with velocity $v_0$ while $B$ is at rest. What is the distance moved by $A$ relative to $B$ before they move with the same velocity?

$A$ particle of mass $7 \, kg$ moving at $5 \, m/s$ is acted upon by a variable force opposite to its initial direction of motion. The variation of force $F$ with time $t$ is shown in the graph.