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

$\frac{R}{r}$

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$\frac{r}{R}$

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$\frac{R^{2}}{r^{2}}$

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$\frac{r^{2}}{R^{2}}$

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Solution

The correct option is C $\frac{R}{r}$
Angular velocity is given by, $ω = \frac{2 π}{T}$
Centripetal acceleration is given by, $a = ω^{2} r$

$\frac{a_{R}}{a_{r}} = \frac{ω_{R}^{2} \times R}{ω_{r}^{2} \times r} = \frac{T_{r}^{2}}{T_{R}^{2}} \times \frac{R}{r} = \frac{R}{r} [A s T_{r} = T_{R}]$

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

The correct option is C RrAngular velocity is given by, ω=2πT Centripetal acceleration is given by, a=ω2r aRar=ω2R×Rω2r×r=T2rT2R×Rr=Rr [As Tr=TR]

The correct option is C $\frac{R}{r}$
Angular velocity is given by, $ω = \frac{2 π}{T}$
Centripetal acceleration is given by, $a = ω^{2} r$

$\frac{a_{R}}{a_{r}} = \frac{ω_{R}^{2} \times R}{ω_{r}^{2} \times r} = \frac{T_{r}^{2}}{T_{R}^{2}} \times \frac{R}{r} = \frac{R}{r} [A s T_{r} = T_{R}]$