Q. 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) 10.5%
Explanation
(d) $T = 2\pi\sqrt{\frac{l}{g}}$
$\Rightarrow$ $\frac{\mathrm{\Delta}T}{T} = \frac{1}{2}\ \frac{\mathrm{\Delta}l}{l}$
Given, $\frac{\mathrm{\Delta}l}{l} = 21\%$
$\therefore$ $\frac{\mathrm{\Delta}T}{T} = \frac{1}{2} \times 21\% = 10.5\%$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.