Question

The length of a simple pendulum is increased by 1%. Its time period will

• A. increase by 1%
• B. increase by 0.5%
• C. decrease by 0.5%
• D. increase by 2%.

Answer 1

The correct option is B

increase by 0.5%

1. As we know, the time period of a simple pendulum, where l is the length of a pendulum and g is the acceleration due to gravity.
2. Therefore, $T\alpha \sqrt{l}$
3. $\Rightarrow \frac{∆T}{T}=\frac{1}{2}\frac{∆l}{l}$
4. $∆T$ is change in the time period and $∆l$ is change (increase) in the length of the pendulum.
5. Given, $∆l=1\%0fl=0.01l$
6. So, $\frac{∆T}{T}=\frac{1}{2}\frac{0.01l}{l}=0.005$
7. $\Rightarrow ∆T=0.005\times T=0.5\%ofT$.

Hence, the correct option is B.