Question

The time periods of two simple pendulums at a place are in the ratio 2:1. What will be the corresponding ratio of their lengths?

Answer 1

Let T₁ and T₂ be the time periods of the two pendulums of lengths l₁ and l₂, respectively.

Then, we know that the time period is directly proportional to the square root of the length of the pendulum.

∴  `T_1/T_2 = sqrt(l_1/l_2)`

or , `l_1/l_2 = (T_1/T_2)^2`

or , `l_1/l_2 = (2/1)^2 = 4 : 1`