A cyclist is moving on a circular path with a constant speed, the value of normal reaction for the complete path

A small block slides down from the top of hemisphere of radius $R=3 \mathrm{m}$ as shown in the figure. The height $h$ at which the block will lose contact with the surface of the sphere is $m$. (Assume there is no friction between the block and the hemisphere)

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 body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $AB=D$. The height $h$ is equal to,

A bullet of $10 \mathrm{g}$, moving with velocity $v$, collides head-on with the stationary bob of a pendulum and recoils with velocity $100 \mathrm{m} {\mathrm{s}}^{-1}$. The length of the pendulum is $0.5 \mathrm{m}$ and mass of the bob is $1 \mathrm{kg}$. The minimum value of $v \text{in} \mathrm{m} {\mathrm{s}}^{-1}$, so that the pendulum describes a circle. (Assume the string to be inextensible and $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

A sphere of mass $\text{'}m\text{'}$ is attached to a spring of spring constant $\text{'}k\text{'}$ and is held in unstretched position over an inclined plane as shown in the figure. After letting the sphere go, find the maximum length by which the spring extends, given the sphere only rolls.

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 $g=9.8{ \mathrm{m} \mathrm{s}}^{-2}$)