Question

The ratio of frequencies of oscillation for two simple pendulums are $2:3$, then their respective lengths are in ratio:

• A. $\sqrt{\frac{2}{3}}:1$
• B. $\sqrt{\frac{3}{2}}:1$
• C. $4:9$
• D. $9:4$

Answer 1

The correct option is D $9:4$

Frequency of oscillation of simple pendulum is $f=\frac{1}{T}$
$\Rightarrow f=\frac{1}{2\pi }\sqrt{\frac{g}{l}}$
$\Rightarrow f\propto \frac{1}{\sqrt{l}}$
$\Rightarrow \frac{f_1}{f_2}=\sqrt{\frac{l_2}{l_1}}$
$\Rightarrow \frac{l_1}{l_2}={\left(\frac{f_2}{f_1}\right)}^2={\left(\frac{3}{2}\right)}^2=\frac{9}{4}$ $\because (f_1:f_2=2:3)$,
$\Rightarrow l_1:l_2=9:4$