In the given figure the co-efficient of friction between the block and the incline plane is $\text{'}1\text{'}.$ The acceleration with which the system should be accelerated so that the friction between the block and the wedge becomes zero $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$ is

A force of $49 \mathrm{N}$ is just able to move a block of wood weighing $10 \mathrm{kg}$on a rough horizontal surface, then coefficient of friction is

Find the compression in the spring if the system shown below is in equilibrium.

All surfaces shown in the figure are frictionless. A block of mass $2 \mathrm{kg}$ is kept on a wedge of mass $10 \mathrm{kg}.$ If the mass $m$ remains stationary w.r.t. wedge, the magnitude of force $P$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A circular track of radius $600 \mathrm{m}$ is to be designed for vehicles passing at an average speed of $54 \mathrm{km} {\mathrm{hr}}^{–1}.$ The required angle of banking is

Figure shows a small bob of mass $m$ suspended from a point on a thin rod by a light inextensible string of length $l.$The rod is rigidly fixed on a circular platform. The platform is set into rotation. The minimum angular speed $\omega ,$ for which the bob loses contact with the vertical rod, is

The whole set up shown in the figure is rotating with constant angular velocity $\omega$ on a horizontal frictionless table. The ratio of tensions $\frac{T_1}{T_2}$ is ( Given, $\frac{I_2}{I_1}=\frac{2}{1}$ )