A ball is released from rest from point $P$ of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point $Q$ is $A$ while angular position of point $Q$ is $\alpha$ with respect to point $P$. Which of the following graphs represent the correct relation between $A$ and $\alpha$ when ball goes from $Q$ to $R$?

A pendulum of length $2 \mathrm{m}$ consists of a wooden bob of mass $50 \mathrm{g}$. A bullet of mass $75 \mathrm{g}$ is fired towards the stationary bob with a speed $v$. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of $v$ is _____  $\mathrm{m} {\mathrm{s}}^{-1}$

(Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$).

A pendulum is suspended by a string of length $250 \mathrm{cm}$. The mass of the bob of the pendulum is $200 \mathrm{g}$. The bob is pulled aside until the string is at $60°$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be _____ $\mathrm{m} {\mathrm{s}}^{-1}$. (if $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

In the given figure, the block of mass $m$ is dropped from the point $A$. The expression for kinetic energy of block when it reaches point $B$ is