Question

The length of a simple pendulum executing simple harmonic motion is increased by $21\%$.The percentage increase in the time period of the pendulum of increased length is.

• A. $11\%$
• B. $21\%$
• C. $42\%$
• D. $10\%$

Answer 1

The correct option is D $10\%$

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

where $L$ is the length of the string.

New length of the string $L^{\prime }=L+\frac{21}{100}L=1.21L$

Thus new time period of the pendulum $T^{\prime }=2\pi \sqrt{\frac{L^{\prime }}{g}}$

$T^{\prime }=2\pi \sqrt{\frac{1.21L}{g}}$

Now $\frac{T^{\prime }-T}{T}\times 100=\frac{\sqrt{1.21}-1}{1}\times 100=10$

Thus time period is increased by 10 %.