Question

The ratio of frequencies of two pendulums are 2:3, then their length are in ratio

• A. $\sqrt{2/3}$
• B. $\sqrt{3/2}$
• C. $4/9$
• D. $9/4$

Answer 1

The correct option is D $9/4$

The frequency of oscillation is given by:

$n=\frac{1}{2\pi }\sqrt{\frac{l}{g}}$

So,

Frequency $n\propto \frac{1}{\sqrt{1}}$

$\Rightarrow \frac{n_1}{n_2}=\sqrt{\frac{l_2}{l_1}}$

$\Rightarrow \frac{l_1}{l_2}=\frac{n_2^2}{n_1^2}=\frac{9}{4}$