Question

What is the ratio the time periods of two pendulums at a given place, when their lengths are $64cm$ and $256cm$ respectively.

• A. $1:2$
• B. $1:3$
  
• C. $3:4$
• D. $4:7$

Answer 1

The correct option is A $1:2$

Time period of simple pendulum is given by

$T=2\pi \sqrt{\frac{l}{g}}$

$L_1=6$ and $L_2=256$

$\therefore \frac{T_1}{T_2}=\sqrt{\frac{L_1}{L_2}}$

$\Rightarrow \frac{T_1}{T_2}=\frac{1}{2}$