Question

Two pendulums of lengths 1.44 and 1 metre length start swinging together. After how many vibrations they will again start swing together?

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is D 6

We know ,

$T\propto \sqrt{L}$ \\ where L is the length of the pendulum .

Let $T_1$ be the time period of the longer pendulum and $T_2$ be the time period of the shorter pendulum .

Thus, $\frac{T_1}{T_2}=\sqrt{\frac{L_1}{L_2}}$

Or, $\frac{T_1}{T_2}=\sqrt{\frac{1.44}{1}}$

Or, $\frac{T_1}{T_2}=\frac{1.2}{1}$

Or , $\frac{T_1}{T_2}=\frac{12}{10}$

Or, $5T_1=6T_2$

Therefore 5 vibrations of the longer pendulum is equal to six vibrations of the shorter pendulum .