Question

The length of a simple pendulum for a given time period is $l$. if the pendulum is taken to a place where acceleration due to gravity is doubled, the for the time period to remain the same its length should be:

• A. $2l$
• B. $l$
• C. $\frac{l}{2}$
• D. $\frac{l}{4}$

Answer 1

The correct option is A $2l$

The time period of a simple pendulum is,

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

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

from the above equation,

The length of the simple pendulum is directly proportional to acceleration due to gravity. If acceleration due to gravity is double then the length of the pendulum is also double.

$l^{\prime }=2l$

The