A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break

In a circus stuntman rides a motorbike in a circular track of radius $R$ in the vertical plane. The minimum speed at highest point of track will be

A bead of mass $\frac {1}{2}\,kg$ starts from rest from $A$ to move in a vertical plane along a smooth fixed quarter ring of radius $5\,m$, under the action of a constant horizontal force $F = 5\,N$ as shown. The speed of bead as it reaches the point $B$ is ……………. $\mathrm{m}/ \mathrm{s}$ [Take $g = 10\,m/s^2$ ]

A particle of mass $m$ , attached with a string of length $l$ is moving in a vertical circle. If the particle is just looping the loop without slackening of the string and $v_A, v_B, v_D$ are speeds at positions $A, B, D$ shown in figure, then

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 $g =10 \; m / s ^{2}$ )