Question

When two pendulums $X$ and $Y$ of time period $4s$ and $4.2 \,s$ are made to vibrate simultaneously. They are initially in phase. After how many vibrations, they will be in the same phase?

• A. 25
• B. 30
• C. 35
• D. 21

Answer 1

Answer: (D)

Pendulum having greater time period makes one oscillation less than the other. Time period of pendulum $X$ is $4 s$. Time period of pendulum $Y$ is $4.2 s$. If $X$ makes $n$ oscillation, then $Y$ makes $(n-1)$ oscillations.
Time taken by $X$ to make $n$ oscillation
$=4 n$ ... (i)
Similarly, time taken by $Y$ to make $(n-1)$ oscillations
$=4.2(n-1)$ ... (ii)
Equating Eqs. (i) and (ii), we get
$\Rightarrow 4.2 n-4.2=4 n $
$ \Rightarrow 4.2 n-4 n=4.2 $
$ \Rightarrow 0.2 n=4.2 $
$ \Rightarrow n=\frac{4.2}{0.2} $
$\therefore n=21$