Question

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

Answer

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As we know,

T = 2 \pi \sqrt{l\over g}

Time period is directly proportional to the square root of the length of the pendulum.

In the case when,

T1 : T2 = 2 : 1  ….. [Equation 1]

we know that,

T1 : T2 = √l1 : √l2  ……. [Equation 2]

So we get,

√l1 : √l2 = 2 : 1

Squaring both sides we get,

l1 : l2 = 4 : 1

Hence, ratio of lengths = 4 : 1

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