Explanation

(d) The time period ($T$) of a simple pendulum length $l$, is given by
$T = 2\pi\sqrt{\frac{l}{g}} = \frac{1}{frequency(n)}$
where $g$ is acceleration due to gravity.
$\therefore$ $\frac{n_{1}}{n_{2}} = \sqrt{\frac{l_{2}}{l_{1}}}$
$\Rightarrow$ $\frac{l_{1}}{l_{2}} = \left( \frac{n_{2}}{n_{1}} \right)^{2}$
Given, $\frac{n_{2}}{n_{1}} = \frac{3}{2}$
$\therefore$ $\frac{l_{1}}{l_{2}} = \left( \frac{3}{2} \right)^{2} = \frac{9}{4}$