Question

Two pendulums at rest start swinging together. Their lengths are respectively $1.44m$ and $1m$. They will again start swinging in the same phase together after _______ of the longer pendulum.

• A. $1$ vibration
• B. $3$ vibrations
• C. $4$ vibrations
• D. $5$ vibrations

Answer 1

The correct option is D $5$ vibrations

Let, $T_{1}and{T}_2$ time period of 1st and 2nd pendulum.

We know, $T=\sqrt{L}$

$\frac{T_1}{T_2}=\sqrt{\frac{1.44}{1}}=\sqrt{\frac{144}{100}}=\frac{12}{10}\Rightarrow 5T_1=6T_2$

Hence time taken 5 complete vibration by longer is equal to the time taken by 6 complete vibration by shorter.