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 $(\text{100}\text{l}\text{)}$ and $(\text{121}\text{l})$
Since we know the time period of a simple pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$
$\therefore$ $\frac{{\text{T}}^{{}^{\prime }}}{\text{T}}=\sqrt{\frac{121}{\text{100}}}=\frac{11}{10}$
$\therefore$ Fractional change = $\frac{{\text{T}}^{{}^{\prime }}-\text{T}}{\text{T}}=\frac{11-10}{10}=\frac{1}{10}$
$\therefore$ Percentage change = $10\%$