First slide

The two types of acceleration

Question

Two bodies of masses 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 accelerations is

Easy

A

R / r
B

r / R
C

R² / r²
D

r² / R²

Solution

$a_{c} = \frac{V^{2}}{r} = \frac{(rω)^{2}}{r} = {rω}^{2}$
$\begin{array}{l} a_{c} = (4 π^{2} r / T^{2}) (∵ ω = 2 π / T) \\ {(a_{c})}_{1} = (4 π^{2} R / T^{2}) and {(a_{c})}_{2} = (4 π^{2} r / T^{2}) \\ ∴ \frac{{(a_{c})}_{1}}{{(a_{c})}_{2}} = \frac{R}{r} \end{array}$

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