Question

A simple pendulum of length $l_{1}$, has a time period of $4 \,s$ and another simple pendulum of length $l_{2}$ has a time period $3 \,s$. Then the time period of another pendulum of length $\left(l_{1}-l_{2}\right)$ is

• A. $\sqrt{3}\, s$
• B. $1\, s$
• C. $\sqrt{\frac{3}{4}} \,s$
• D. $\sqrt{7} \,s$

Answer 1

Answer: (D)

$ 4\, s =2 \pi \sqrt{\frac{l_{1}}{g}}$ or $l_{1}=\frac{4 g}{\pi^{2}}$
$3 \,s =2 \pi \sqrt{\frac{l_{2}}{g}}$ or $l_{2}=\frac{9 g}{4 \pi^{2}}$
$\left(l_{1}-l_{2}\right)=\frac{g}{\pi^{2}}\left(4-\frac{9}{4}\right)=\frac{7 g}{4 \pi^{2}}$
$T^{\prime}=2 \pi \sqrt{\frac{\left(l_{1}-l_{2}\right)}{g}}=2 \pi \sqrt{\frac{7 g}{4 \pi^{2} g}}=\sqrt{7} \,s$