Question

Two simple pendulums $A$ and $B$ of time periods $2s$ and $2.1\,s$ are made to vibrate simultaneously. They are initially in phase. After how many vibrations, they will be in the same phase?

• A. 35
• B. 30
• C. 25
• D. 21

Answer 1

Answer: (D)

Pendulum having greater time period makes one oscillation less than the other. Since, both the pendulums will be in same phase after some time,
hence pendulum having greater time period
$ ({{T}_{2}}=2.1\,s) $
makes one oscillation less than the other $ ({{T}_{2}}=2\,s) $ .
Time taken by pendulum $A$ to make $n$ oscillations is $2 \,n$ Time taken by pendulum $ B=2.1\,(n-1) $
Hence, $ 2\,n=2.1\,(n-1) $
$ \Rightarrow n=\frac{2.1}{0.1}=21 $