MCQ
Two pendulums have time periods $T$ and $5T/4.$ They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum they will be again in the same phase :
- ✓$5$
- B$4$
- C$11$
- D$9$
✓
Answer
Correct option: A.
$5$
a
When the pendulum $A$ with time period $\frac{5 T}{4}$ completes phase of $2 \pi$ in $\frac{5 T}{4},$ the other pendulum $B$ leads by phase $\frac{\pi}{2}$.
When the pendulum $A$ with time period $\frac{5 T}{4}$ completes phase of $2 \pi$ in $\frac{5 T}{4},$ the other pendulum $B$ leads by phase $\frac{\pi}{2}$.
So after $4$ oscillations of pendulum $A$ i.e. after $5 T$, pendulum $B$ leads by $2 \pi$ i.e they come in phase.
i.e. after $5$ oscillations of small pendulum (Time taken $=5 T$ ), they will again come in the same phase.
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