A man of mass $m$ is standing in an elevator moving downward with an acceleration $\frac{g}{4}$. The force exerted by the bottom surface of the elevator on the man will be

A vehicle is moving on a road with an acceleration a $=20 \mathrm{m} {\mathrm{s}}^{-2}$ as shown in figure. The frictional coefficient between the block of mass $\left(m\right)$ and the vehicle so that block is does not fall downward is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

In the given arrangement all surfaces are smooth. What acceleration should be given to the system, for which the block $m_2$ doesn't slide down?

A trolley is falling freely on inclined plane as shown in the figure. The angle of string of pendulum with the ceiling of trolley is $\left(\alpha \right)$ equal to

A block of mass $m$ is kept on horizontal turn table at $x$ distance from the centre. If coefficient of friction between block and surface of turn table is $\mu$, then maximum angular speed of the table so that block does not slip is

If trolley accelerates horizontally with acceleration a then bob is displaced backward from its initial vertical position. The angular deflection of the bob in equilibrium is

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