$A$ fighter plane is moving in a vertical circle of radius $r$. Its minimum velocity at the highest point of the circle will be

Length of a simple pendulum is $1 \,m$. When its bob is at its lowest point its velocity is $7 \,ms^{-1}$. If the bob leaves its circular path at a height $h$ above the centre of the circle, then the value of $h$ is $(g=10 \,ms^{-2})$. (in $\,m$)

$A$ body of mass $m$ attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is ($g =$ gravitational acceleration).

$A$ bullet of mass $m$ moving with velocity $v$ passes through a pendulum bob of mass $M$ and emerges with a velocity $v/2$. What is the minimum value of $v$ so that the pendulum bob completes a full vertical circle of length $\ell$?

In the case of vertical circular motion of a particle attached to a thread of length $r$, if the tension in the thread is zero at an angle of $30^{\circ}$ with the horizontal as shown in the figure, the velocity at the bottom point $(A)$ of the circular path is ($g =$ gravitational acceleration).

$A$ particle is tied to a $20 \ cm$ long string. It performs circular motion in a vertical plane. What is the angular speed of the particle when the tension in the string at the top is zero? (Take $g = 9.8 \ m/s^2$)