Question

The time periods of two pendulums are 4.8 s and 1.2 s. Calculate the ratio of their acceleration due to gravities.

Answer 1

Question :

The time periods of two similar simple pendulums are 4.8 s and 1.2 s. Calculate the ratio of their acceleration due to gravities.

Solution :

Since the two pendulums are similar, their lengths are equal.

$T = 2\pi \sqrt{ \frac{l}{g} }$

For similar pendulums, l is same so,

$T \propto \frac{1}{ \sqrt{g} }$

Given, Time periods of two pendulums are 4.8s, and 1.2s

$\frac{T _{1} }{T _{2}} = \sqrt{\frac{g _{2}}{ {g} _{1}} }$

Therefore,

$\frac{g _{1}}{ {g} _{2}} = (\frac{T _{2} }{T _{1}}) ^{2}$

So,

$\frac{g _{1}}{ {g} _{2}} = (\frac{1.2 }{4.8}) ^{2} \\ \\ \frac{g _{1}}{ {g} _{2}} = ( \frac{1}{4} ) ^{2} = \frac{1}{16}$

Therefore, The ratio of their acceleration due to gravity is 1 : 16