Question

The time periods of two simple pendulums of different lengths are the same on two different planets. If the lengths of the two pendulums are in the ratio of $1:9$, then the ratio of the accelerations due to gravity on the two planets, most likely, is :

• A. $1:3$
• B. $1:9$
• C. $3:1$
• D. $9:1$

Answer 1

Answer: (B)

. $1:9$.

The time period ($T$) of a pendulum of length ($l$) is given by,

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

where $g$ is the acceleration due to gravity.

Here, time period , $T_1=T_2$

$T_1=2\pi \sqrt{\frac{l_1}{g_1}}$ and $T_2=2\pi \sqrt{\frac{l_2}{g_2}}$

Thus, $\sqrt{\frac{l_1}{g_1}}$$=\sqrt{\frac{l_2}{g_2}}$ (as $T_1=T_2)$

or $\frac{g_1}{g_2}=\frac{l_1}{l_2}=\frac{1}{9}$