The upper $\left(\frac{1}{n}\right)$ th of an inclined plane is smooth and the remaining lower part is rough with coefficient of friction $\mu_k$. If a body starting from rest at the top of the inclined plane will again come to rest at the bottom of the plane, then the angle of inclination of the inclined plane is

A spring of spring constant $200 \mathrm{~N}-\mathrm{m}^{-1}$ is initially stretched by 10 cm from the unstretched position. The work to be done to stretch the spring further by another 10 cm is

A $4 \mathrm{~kg}$ mass is suspended as shown in figure. All pulleys are frictionless and spring constant $k$ is $8 \times 10^3 \mathrm{Nm}^{-1}$. The extension in spring is $\left(g=10 \mathrm{~ms}^{-2}\right)$

Two bodies $A$ and $B$ of masses $2 m$ and $m$ are projected vertically upwards from the ground with velocities $u$ and $2 u$ respectively. The ratio of the kinetic energy of body $A$ and the potential energy of body $B$ at height equal to half of the maximum height reached by body $A$ is