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

Block of $3\,kg$ is initially in equilibrium and is hanging by two identical springs $A$ and $B$ as shown in figures. If spring $A$ is cut from lower point at $t=0$ then, find acceleration of block in $ms ^{-2}$ at $t =0$.

A coin is dropped in a lift. It takes time $t_1$ to reach the floor when lift is stationary. It takes time $t_2$ when lift is moving up with constant acceleration, then

A force $\vec{F}=\hat{i}+4 \hat{j}$ acts on block shown. The force of friction acting on the block is

A light string passing over a smooth light pulley connects two block of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $(\frac {g}{8})$, then the ratio of masses is