Question

Two simple pendulums $A$ and $B$ are made to oscillate simultaneously and it is found that $A$ completes $10$ oscillations in $20\, sec$ and $B$ completes $8$ oscillations in $10\, sec$. The ratio of the lengths of $A$ and $B$ is

• A. $\frac{8}{5}$
• B. $\frac{64}{25}$
• C. $\frac{5}{4}$
• D. $\frac{25}{64}$

Answer 1

Answer: (B)

$\frac{64}{25}$

Answer 2

According to questions,
For pendulum $A$.
$T_{A}=2 \pi \sqrt{\frac{l_{A}}{g}}$
$\frac{20}{10}=2 \pi \sqrt{\frac{l_{A}}{g}}\,\,\,\,\,\dots(i)$
For pendulum $B$,
$T_{B}=2 \pi \sqrt{\frac{l_{B}}{g}}$
$\frac{10}{8}=2 \pi \sqrt{\frac{l_{B}}{g}}\,\,\,\,\,\,\dots(ii)$
Dividing E (i) by E (ii), we get
$\frac{l_{A}}{l_{B}}=\left(\frac{160}{100}\right)^{2}$
$\frac{I_{A}}{l_{B}}=\frac{64}{25}$