91Ó°ÊÓ

The figure for the three pendulums is given.

We can predict the period of the pendulum B from torques acting on it. Then comparing arm lengths of A and C we can rank them according to their periods.

Formula:

The period of an oscillation of a pendulum, $T=2\mathrm{Ï€}\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$ (i)

Let’s denote pendulums in the given figure as A, B and C respectively from left to right.

Since equal torques is acting on both the sides of pendulum B, it will have infinite period of oscillation. So, from equation (i), we say that it will havethegreatest period amongst the three.

The time period of pendulum is directly proportional to its arm length. The pendulum C has greater arm length than that of the other pendulums.

Thus, the time period for pendulum C is greater than that for pendulum A.

Hence, we can rank the pendulums as ${\mathrm{T}}_{\mathrm{b}}>{\mathrm{T}}_{\mathrm{c}}>{\mathrm{T}}_{\mathrm{a}}$.