Two blocks $A$ and $B$ of masses $5 \mathrm{kg}$ and $10 \mathrm{kg}$ respectively are pushed on rough surface. The contact force between the blocks is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A block of mass $m$ is placed over a wedge of mass $4 \mathrm{m}$ and the system is acted upon by a horizontal force $F.$ Friction is absent everywhere. The value of $F$ so that the block does not slide over the wedge, is

A uniform rod of mass $M$ and length $L$ is rotated in horizontal plane about a vertical axis with constant angular velocity $\omega$ as shown in figure. The tension in the rod at point $P$ is

In the given arrangement strings and pulley are light and smooth, what should be mass of block $A$ so that it could remain at rest?

In the given arrangement, friction is absent and strings, pulleys are ideal. The difference of tension $\left(T_1-T_2\right)$ is

In the given arrangement what can be the maximum mass of block $C$ so that blocks $A$ and $B$ move together?

In the given arrangement, if the lift is moving upwards with acceleration $\frac{g}{2},$ then force exerted by the string on ceiling is

The acceleration of block $A$ at the given instant is

The acceleration of block $C$ is