Question

If the length of second's pendulum is decreased by 2%, How many seconds it will lose per day?

• A. 3927 sec
• B. 3727 sec
• C. 3427 sec
• D. 864 sec

Answer 1

The correct option is D

864 sec

1. As we know that , 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 in the length of the pendulum.
5. Given, $∆l=2\%0fl=0.02l$
6. So, $\frac{∆T}{T}=\frac{1}{2}\frac{0.02l}{l}=0.01$
7. $\Rightarrow ∆T=0.01\times T=0.01\times 24\times 60\times 60=864$ sec.

Hence, the correct option is D.