The string of a pendulum of length $L$ is displaced through $90^{\circ}$ from the vertical and released. The maximum tension the string must withstand as the pendulum passes through the mean position is ($m =$ mass of the pendulum,$g =$ acceleration due to gravity).

$A$ 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 filled with water is tied to a string of length $4 \ m$ and rotated in a vertical circle. To ensure that the water does not spill,the time period of rotation should be ........ $s$.

$A$ 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 highest position is ............. $m/s$ (Take $g=10\, m/s^2$).

$A$ body of mass $m \ kg$ slides from rest along the curve of a vertical circle from point $A$ to $B$ on a frictionless path. The velocity of the body at $B$ is: (Given: $R = 14 \ m$,$g = 10 \ m/s^2$,and $\sqrt{2} = 1.4$) (in $m/s$)

$A$ bob attached to a string is held horizontal and released. The tension $T$ and vertical distance $h$ from the point of suspension can be represented by which of the following graphs?