If the acceleration of the elevator $a_0>g$, then

A plank inclined at an angle of $\alpha$ to the horizontal lies on two supports $A$ and $B$ (figure), over which it can slip without friction under the action of its own weight $\mathrm{Mg}$. With what acceleration and in what direction should a man of mass $m$ move along the plank so that it should not slip?

In the shown figure inside a fixed hollow cylinder with vertical axis a pendulum is rotating in a conical path with its axis same as that of the cylinder with uniform angular velocity. Radius of cylinder is $30 \mathrm{cm}$, length of string is $50 \mathrm{cm}$ and mass of bob is $400 \mathrm{gm}$. The bob makes contact with the inner frictionless wall of the cylinder while moving

A ball of mass '$m$' rotating in a circle of radius '$r$' with speed $v$ inside a smooth cone as shown in figure. Let $N$ be the normal reaction on the ball by the cone, then choose the correct the option.

The block $A$ and $B$ shown in the figure have masses $M_A=5\mathrm{kg}$and $M_B=4\mathrm{kg}$. The system is released from rest. The speed of $B$ after $A$ has travelled a distance $1\mathrm{m}$ along the incline is:

A gun which fires small ball of mass $20\mathrm{gm}$ is firing $20$ balls per second on the smooth horizontal table surface $ABCD$. If the collision is perfectly elastic and balls are striking at the centre of table with a speed $5 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle of $60°$ with the vertical just before collision, then force exerted by one of the leg on ground is (assume total weight of the table is $0.2\mathrm{kg}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$):-