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)

In the arrangement as shown, tension $T_2$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

In the figure, a ball of mass $m$ is tied with two strings of equal length as shown. If the rod is rotated with angular velocity $\omega$, then

A particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of plane of circle above vertex is $h.$ The speed of particle should be