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)

Let the lengths of the pendulum be $\left(\right.\text{100}\textit{l}\text{)}$ and $\left(\right.\text{121}\textit{l}\left.\right)$
Since we know the time period of a simple pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$
$\therefore $ $\frac{\text{T}^{'}}{\text{T}}=\sqrt{\frac{121}{\text{100}}}=\frac{11}{10}$
$\therefore $ Fractional change = $\frac{\text{T}^{'} - \text{T}}{\text{T}}=\frac{11 - 10}{10}=\frac{1}{10}$
$\therefore $ Percentage change = $10\%$