Q. The length of simple pendulum is increased by 1%. Its time period will
A) increase by 2%
B) increase by 1%
C) increase by 0.5%
D) decrease by 0.5%
Explanation
(c) We have, $T \propto \sqrt{l}$,
$\therefore\frac{T_{1}}{T} = \sqrt{\frac{0.01l}{l}}$
$= \left( 1 + \frac{1}{100} \right)^{1/2} = \left\lbrack 1 + \frac{1}{2 \times 100} \right\rbrack$
$\therefore\%$ increase in time period
$= \left( \frac{T_{1} - T}{T} \right) \times 100$
$= \frac{1}{2 \times 100} \times 100 = 0.5\%$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.