$A$ point mass '$m$' is moved in a vertical circle of radius '$r$' with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is .......... $mg$.

$A$ ball attached to one end of a string swings in a vertical plane such that its acceleration at point $A$ (extreme position) is equal to its acceleration at point $B$ (mean position). The angle $\theta$ is :-

$A$ body of mass $m$ connected to a massless and unstretchable string moves in a vertical circle of radius $R$ under gravity $g$. The other end of the string is fixed at the center of the circle. If the velocity at the top of the circular path is $n\sqrt{gR}$,where $n \geq 1$,then the ratio of the kinetic energy of the body at the bottom to that at the top of the circle is:

$A$ stone of mass $m$,tied to a string,is being whirled in a vertical circle with a uniform speed. The tension in the string is

$A$ bob of mass $m$ is suspended by a light string of length $L$. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes a full vertical circle,reaching the topmost position $B$. The ratio of kinetic energies $\frac{(\text{K.E.})_A}{(\text{K.E.})_B}$ 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).