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)

4 sec

Answer 2

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, $T_2 = 2 T_1 = 4$ sec.