Question

Time period of a simple pendulum is $2\sec$. If its length is increased by $4$ times, then its period becomes

• A. 8 sec
• B. 12 sec
• C. 16 sec
• D. 4 sec

Answer 1

Answer: (D)

Time period of a simple pendulum is given by
$T=2\pi \sqrt{\frac{l}{g}}$
$\Rightarrow T\propto \sqrt{l}$.
$\therefore \frac{T_1}{T_2}=\sqrt{\frac{l_1}{l_2}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$
or, $T_2=2T_1=4\sec .$