Two simple pendulums of length 5m and 10m respectively are given … - Vidyadip

MCQ

Two simple pendulums of length $5m$ and $10m$ respectively are given small linear displacement in one direction at the same time. They will be again in the phase when the pendulum of shorter length has completed oscillations:

A
$1$
✓
$2$
C
$3$
D
$5$

✓

Answer

Correct option: B.

$2$

In case of simple pendulum,
$\text{T}=2\pi\sqrt{\frac{5}{\text{g}}}$ and $\text{T}'=2\pi\sqrt{\frac{10}{\text{g}}}$
$\therefore\text{T}'=2\text{T}$
Let the two pendulums are in same phase for first time when shorter one has completed $n$ oscillations. Then
$\text{nT = (n}-1)\text{T}'$
$\frac{\text{n}}{\text{n}-1}=\frac{\text{T}'}{\text{T}}=\frac{2\text{T}'}{\text{T}}=2$
$\text{n = 2n}-2$
$\text{n}=2$

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