Question

If length of pendulum is increased by 2%. The time period will

• A. increases by 1%
• B. decreases by 1%
• C. increases by 2%
• D. decreases by 2%

Answer 1

The correct option is A increases by 1%

Time period of pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$
Error in time period $\frac{\Delta T}{T}\times 100=\frac{1}{2}\times$ $\frac{\Delta l}{l}\times 100$
Given : $\frac{\Delta l}{l}\times 100=2$%
$⟹$ $\frac{\Delta T}{T}\times 100=\frac{1}{2}\times$ $2=1$%
Hence the time period increases by 1% if the length of pendulum is increased by 2%.