$A$ particle of mass $m$ is released from $a$ height $H$ on $a$ smooth curved surface which ends into a vertical loop of radius $R$, as shown If $\theta$ is instantaneous angle which the line joining the particle and the centre of the loop makes with the vertical, then identify the correct statement $(s)$ related to the normal reaction $N$ between the block and the surface

A pendulum of length $2 \; m$ consists of a wooden bob of mass $50 \; g$. A bullet of mass $75 \; g$ 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 $\dots \; ms ^{-1}$. (if $g =10 \; m / s ^{2}$ )

A body tied to a string of length  $L$  is revolved in a vertical circle with minimum velocity, when the body reaches the upper most point the string breaks and the body moves under the influence of the gravitational field of earth along a parabolic path. The horizontal range  $AC$  of the body will be

A small bob tied at one end of a thin string of length $1\, m$ is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $5: 1 .$ The velocity of the bob at the height position is …………. $m / s$ (Take $\left.g=10 \,m / s ^{2}\right)$