A ring of mass $m=1 \mathrm{kg}$ can slide over a smooth vertical rod. A light string attached to the ring passing over a smooth fixed pulley at a distance of $L=0.7 \mathrm{m}$ from the rod as shown in the figure. At the other end of the string mass $M=5 \mathrm{kg}$ is attached, lying over a smooth fixed inclined plane of inclination angle $37°.$ The ring is held in level with the pulley and released. Determine the instantaneous power of the gravitational force acting on the ring (in watts) when the string makes an angle $\left(\alpha =37°\right)$ with the horizontal. $\left[\sin 37°=0.6\right]$

A mass of  $0.5 \mathrm{kg}$ moving with a speed of $1.5 \mathrm{m} {\mathrm{s}}^{-1}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $\mathrm{k}=50 \mathrm{N} {\mathrm{m}}^{-1}$. The maximum compression of the spring would be

A large block of wood of mass $M=5.99 \mathrm{kg}$ is hanging from two long massless cords. A bullet of mass $m=10 \mathrm{g}$ is fired into the block and gets embedded in it. The (block $+$ bullet) then swing upwards, their center of mass rising a vertical distance $h=9.8 \mathrm{cm}$ before the (block $+$ bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before the collision is: (Take $g=9.8{ \mathrm{m} \mathrm{s}}^{-2}$)