$A$ stone of mass $m$ is tied to a string and is moved in a vertical circle of radius $r$ making $n$ revolutions per minute. The total tension in the string when the stone is at its lowest point is

$A$ bucket containing water is revolved in a vertical circle of radius $r$. To prevent the water from falling down,the minimum frequency of revolution required is ($g =$ acceleration due to gravity).

$A$ bullet of mass $m$ strikes a pendulum-bob of mass $M$ with velocity $u$. It passes through it and emerges out with a velocity $u/2$ from the bob. The length of the pendulum is $\ell$. What should be the minimum value of $u$,if the pendulum-bob will swing through a complete circle?

$A$ sphere is suspended by a thread of length $l$. What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension point?

$A$ body of mass $m$ hangs at one end of a string of length $l$,the other end of which is fixed. It is given a horizontal velocity such that the string just reaches a position where it makes an angle of $60^{\circ}$ with the vertical. The tension in the string at the mean position is:

$A$ particle of mass $100 \ g$ is performing vertical circular motion as shown in the figure. Find the tangential acceleration at the given position in $m/s^2$. (Take $g = 10 \ m/s^2$)