A block can slide on a smooth inclined plane of inclination $\theta $ kept on the floor of a lift. When the lift is descending with an acceleration $'a'$ . Then the acceleration of the block relative to the incline is

A man of mass $m_1$ is standing on a platform of mass $m_2$ kept on a smooth  horizontal surface. If the man starts moving on the platform with a velocity $v$ relative to the  platform, then recoil velocity of platform is

In the figure the tension in the diagonal string is $60\,N$.

Find the magnitude of the horizontal force $\overline{ F }_1$ and $\overline{ F }_2$ that must be applied to hold the system in the position shown.

Select correct statement regarding pseudo force

For the equilibrium of a body on an inclined plane of inclination $45^{\circ}$. The coefficient of static friction will be

A constant force $F$ is applied in horizontal direction as shown. Contact force between $M$ and $m$ is $N$ and between $m$ and $M ^{\prime}$ is $N ^{\prime}$ then