When the length of the string of a simple pendulum is its period is \(0.5 \pi\) seconds. The period when the length is increased to \(4 l\) will be ____________
Explanation
The period of oscillation is directly proportional to the square root of the length of a simple pendulum i.e.
\(T a \sqrt{l}\),
\(T=K \sqrt{1}, K=\frac{T}{\sqrt{l}}\)
Therefore,
\begin{aligned}
&\frac{T_{1}}{\sqrt{L_{1}}}=\frac{T_{2}}{\sqrt{1}}, T_{2}=\frac{T_{1} \times \sqrt{L_{2}}}{\sqrt{L_{1}}} \\
&=\frac{0.5 \pi^{\circ} \times \sqrt{4 L}}{\sqrt{L}}=\pi \text { secs }
\end{aligned}