Question

Two pendulums differ in lengths by $22cm$. They oscillate at the same place so that one of them makes $30$ oscillations and the other makes $36$ oscillations during the same time. The lengths (in cm) of the pendulums are

• A. $72$ and $50$
• B. $60$ and $38$
• C. $50$ and $28$
• D. $80$ and $58$

Answer 1

The correct option is A $72$ and $50$

Given,

$T_1=\frac{1}{30}$

$T_2=\frac{1}{36}$

The time period of the pendulum is given by

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

$T\propto \sqrt{l}$

$\frac{T_1}{T_2}=\sqrt{\frac{l_1}{l_2}}=\frac{36}{30}$

$\sqrt{\frac{l_1}{l_2}}=\frac{6}{5}$

$\frac{l_1}{l_2}=\frac{36}{25}$. . . . . .(1)

Accorrding to question,

$\frac{11}{25}=\frac{l_1-l_2}{l_2}=\frac{22}{l_2}$. . . . .(2)

From equation (1) and (2), we get

$l_2=50cm$

$l_1=72cm$

The correct option is A.