Question 192: Work, Energy and Power & Circular Motion

Question

Two bodies of mass 10 kg and 5 kg are moving in concentric circular orbits of radii ' R ' and ' r ' respectively such that their periods are same. The ratio between their centripetal acceleration is

Accepted Answer

Step 1: Formula for centripetal acceleration
Centripetal acceleration is
$ a_c = \frac{v^2}{r} = \frac{4 \pi^2 r}{T^2} $
where $T$ is the time period, $r$ is radius.
Step 2: Since the time period is the same
$ a_c \propto r $
So the centripetal acceleration is directly proportional to the orbit radius if the period is the same.
Step 3: Ratio
For body of mass $10 \, 	ext{kg}$ with orbit radius $R$:
$ a_1 = \frac{4 \pi^2 R}{T^2} $
For body of mass $5 \, 	ext{kg}$ with orbit radius $r$:
$ a_2 = \frac{4 \pi^2 r}{T^2} $
Hence their ratio:
$ \frac{a_1}{a_2} = \frac{R}{r} $
Final Answer:
$ \boxed{	frac{R}{r}} $
Correct option: A ($R/r$)

Answer

$\mathrm{R} / \mathrm{r}$

Answer

$\quad \mathrm{r} / \mathrm{R}$

Answer

$\mathrm{R}^2 / \mathrm{r}^2$

Answer

$r^2 / R^2$

Work, Energy and Power & Circular Motion

Two bodies of mass 10 kg and 5 kg are moving in concentric circular orbits of radii ' R ' and ' r ' respectively such that their periods are same. The ratio between their centripetal acceleration is

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