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

A force of $\left(6 x^2-4 x+3\right) \mathrm{N}$ acts on a body of mass 0.75 kg and displaces it from $x=2 \mathrm{~m}$ to $x=5 \mathrm{~m}$. The work done by the force is

A spring of $5 \times 10^3 \mathrm{Nm}^{-1}$ spring constant is stretched initially by 10 cm from unstretched position. The work required to stretch it further by another 10 cm is

A small disc of mass $$m$$ slides down with initial velocity zero from the top $$(A)$$ of a smooth hill of height $$H$$ having a horizontal portion $$(BC)$$ as shown in the figure. If the height of the horizontal portion of the hill is $$h$$, then the maximum horizontal distance covered by the disc from the point $$D$$ is