Question

A simple pendulum whose length is slightly less than that of a seconds pendulum start vibrating with another seconds pendulum in the same phase. After 18 seconds, they again vibrate in the same phase. The periodic time of simple pendulum is-

• A. 0.9 sec
• B. 1.8 sec
• C. 1.4 sec
• D. 1.6 sec

Answer 1

The correct option is B 1.8 sec

It is mentioned that, simple pendulum whose length is slightly less than that of seconds pendulum starts vibrating with another seconds pendulum after 18 seconds they again vibrate in the same phase. Let $T=18s$ , the time period of the simple pendulum is 2 s,$T_1=2$ s .

We need to find the periodic time of simple pendulum .

Let $T_x$ Be the Periodic time of the simple pendulum .

Period $=\frac{1}{Timeperiod}$

Therefore, $\frac{1}{T}=\frac{1}{T_x}-\frac{1}{T_1}$

Or , $\frac{1}{T_x}=\frac{1}{T}+\frac{1}{T_1}$

Or, $\frac{1}{T_x}=\frac{1}{18}+\frac{1}{2}$

Or, $\frac{1}{T_x}=\frac{10}{18}$

Or, $T_x=1.8secs$.