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

Answer: (A)

10%

Answer 2

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= $\frac{T_{2} - T_{1}}{T_{1}} \times 100 = 10\%$