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. $10\%$
• D. $10.5\%$

Answer 1

Answer: (C)

Given,

$\frac{l_2}{l_1}=1.21$

The time period of the simple pendulum executing simple harmonic motion is given by

$T=2\pi \sqrt{\frac{l}{g}}$

$T\propto \sqrt{l}$

$\frac{T_2}{T_1}=\sqrt{\frac{l_2}{l_1}}=\sqrt{1.21}$

$T_2=1.1T_1$

The % increase in time period, $=\frac{T_2-T_1}{T_1}\times 100$

% increase $\frac{1.1T_1-T_1}{T_1}\times 100=10$%