Question

A simple pendulum is executing simple harmonic motion with a time period T. If the length of the pendulum is increased by $21\%,$ the percentage increase in the time period of the pendulum of increased length is

• A. 10%
• B. 21%
• C. 30%
• D. 50%

Answer 1

The correct option is A 10%

If initial length $l_1=100$ then $l_2=121$
By using $T=2\pi \sqrt{\frac{l}{g}}\Rightarrow \frac{T_1}{T_2}=\sqrt{\frac{l_1}{l_2}}$

Hence, $\frac{T_1}{T_2}=\sqrt{\frac{100}{121}}\Rightarrow T_2=1.1T_1$
% increase $=\frac{T_2-T_1}{T_1}\times 100=10\%$