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

Answer 1

The correct option is D $\frac{64}{25}$

Time period of simple pendulum $T=2\pi \sqrt{\frac{l}{g}}$

$⟹$ $\frac{l_A}{l_B}=(\frac{T_A}{T_B}{)}^2$

Time period of pendulum A $T_A=\frac{20}{10}=2$ seconds

Time period of pendulum B $T_B=\frac{10}{8}=\frac{5}{4}$ seconds

Thus ratio of lengths $\frac{l_A}{l_B}=(\frac{2}{\frac{5}{4}}{)}^2=\frac{64}{25}$