A simple pendulum of length ' $l$ ' has a brass bob attached at its lower end. It's period is ' $T$ '. A…
A simple pendulum of length ' $l$ ' has a brass bob attached at its lower end. It's period is ' $T$ '. A steel bob of the 'same size, having density ' x ' times that of brass, replaces the brass bob. Its length is then so changed that the period becomes ' 2 T '. What is the new length?
$4 / x$
$\frac{4 l}{x}$
$4 l$
$2 l$
Solution
$\begin{aligned}
& \mathrm{T}=2 \pi \sqrt{\frac{l}{\mathrm{~g}}} \\
& \Rightarrow \mathrm{~T} \propto \sqrt{l} .
\end{aligned}$ Time period depends only on effective length. Density has no effect on time period. If time period is made 2 times, then length becomes $4 l$