Two wooden blocks are moving on a smooth horizontal surface such that the mass $m$ remains stationary with respect to the block of mass $M$ as shown in figure. The magnitude of force $P$ is

A man is raising himself as well as the crate on which he stands with an acceleration of $5 \mathrm{m} {\mathrm{s}}^{-2}$ by a massless rope-and-pulley arrangement. Mass of the man is $100 \mathrm{kg}$ and that of the crate is $50 \mathrm{kg}$. If $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, then the tension in the rope is

A small block of mass $m$ rests on a smooth wedge of angle $\theta$. With what horizontal acceleration $a$ should the wedge be pulled, as shown in figure, so that the block falls freely?

In the given figure, the acceleration of $A$ is $\overrightarrow{a_A}=15\hat{\mathrm{i}}+15\hat{\mathrm{j}}$. Then the acceleration of $B$ is ($A$ remains in contact with $B$)

In the given figure, the mass $m_2$ starts with velocity $v_0$ and moves with constant velocity on the surface. During motion, the normal reaction between the horizontal surface and fixed triangle block $m_1$ is $N$. Then during motion 

In the given figure, blocks $A$ and $B$ move with velocities $v_1$ and $v_2$ along horizontal direction. Find the ratio of $\frac{v_1}{v_2}$.

If block $B$ moves towards right with acceleration $b$, find the net acceleration of block $A$.

If the blocks $A$ and $B$ are moving towards each other with accelerations $a$ and $b$ as shown in figure, then find the net acceleration of block $C$.