Question

If the length of simple pendulum is increased by $300\%$,then the time period will be increased by

• A. $100\%$
• B. $200\%$
• C. $300\%$
• D. $400\%$

Answer 1

The correct option is A $100\%$

Let intial length $l_1=100$

Final length $l_2=400$

$\frac{T_1}{T_2}=\sqrt{\frac{l_1}{l_2}}\Rightarrow \frac{T_1}{T_2}=\sqrt{\frac{100}{400}}$

$\Rightarrow T_2=2T_1$

Hence $\%$ increase $=\frac{T_2-T_1}{T_1}\times 100=100\%$