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

Answer: (D)

$10\%$

Answer 2

Time period of simple pendulum is given by. $T=2\pi\sqrt{\frac{\ell}{d}}$ New length $\ell '=\ell+\frac{21}{100}\ell=\frac{21}{199}\ell$ $\therefore \frac{T '}{T}=\sqrt{\frac{\ell' }{\ell}}=\sqrt{\frac{21}{100}}$ $\frac{T '}{T}=\frac{11}{10}$ $\Rightarrow T '=T+\frac{1}{10}T$ $T\ne10\%$ of $T.$