The ratio of frequencies of two oscillating pendulums are $3: 2$. Their lengths are in the ratio
The ratio of frequencies of two oscillating pendulums are $3: 2$. Their lengths are in the ratio
$\sqrt{2}: \sqrt{3}$
$9: 4$
$\sqrt{3}: \sqrt{2}$
$4: 9$
Solution
The frequency of oscillation is given by:
$\mathrm{n}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{g}}{\mathrm{L}}}$
So, Frequency $\mathrm{n} \propto \frac{1}{\sqrt{\mathrm{L}}}$
$\Rightarrow \frac{\mathrm{n}_1}{\mathrm{n}_2}=\sqrt{\frac{\mathrm{L}_2}{\mathrm{~L}_1}}$
$\Rightarrow \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{\mathrm{n}_2^2}{\mathrm{n}_1^2}=\frac{4}{9}$