$A$ $10 \, kg$ ball attached to the end of a rigid massless rod of length $L = 1 \, m$ rotates at a constant speed in a horizontal circle of radius $r = 0.5 \, m$ and period $T = 1.57 \, s$ as shown in the figure. The force exerted by the rod on the ball is ........ $N$.

Two balls of masses $m_1$ and $m_2$ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly,the powder charge explodes and the masses are pushed apart. The mass $m_1$ travels a distance $s_1$ and stops. If the coefficients of friction between the balls and the ground are the same,the mass $m_2$ stops after travelling the distance:

The driver of a car travelling at velocity $v$ suddenly sees a broad wall in front of him at a distance $d$. He should

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. When a person walks on a rough surface,the direction of the frictional force exerted by the surface on the person is in the same direction as his motion.
$B$. When a cycle is in motion,the force of friction exerted by the ground on the front wheel is in the backward direction.

Two beads connected by a massless inextensible string are placed over a fixed ring as shown in the figure. The mass of each bead is $m$,and there is no friction between bead $B$ and the ring. Find the minimum value of the coefficient of friction between bead $A$ and the ring so that the system remains in equilibrium. ($C$ is the center of the ring,and the line $AC$ is vertical.)

What force should be applied on the wedge so that the block over it does not move? (All surfaces are smooth)