A simple pendulum \(0.6 m\) long has a period of \(1.55\), what is the period of a similar pendulum \(0.4\) long in the same direction
A. \(1.4 \sqrt{\frac{1}{3}}\)s
B. \(1.5 \sqrt{\frac{1}{3}}s\)
C. \(2.25\)s
D. \(1.00\)s
E. \(2.00\)s
Correct Answer: E
Explanation
\( l_{1}=0.6, T_{1}=1.55, l_{2}=0.4, T_{2}=\) ?
We recall here that
$$
\begin{aligned}
T &=2 \pi \sqrt{\frac{l}{g}} \text { i.e. } T \alpha \sqrt{l} ; \frac{T_{1}}{\sqrt{l_{1}}}=\frac{T_{2}}{\sqrt{l_{2}}} \\
T_{2} &=\sqrt{\frac{l_{2}}{l_{1}}} \times T_{1} \\
&=\sqrt{\frac{0.4}{0.6}} \times 1.55=1.27 sec
\end{aligned}
$$
