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If the law of gravity were inverse law instead of inverse square law, considering two satellites of
same mass but in orbits of radii “ $r$ ” and “ $2 r$ ” around the earth :

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The ratio of speeds of two satellites would be 1 : 1

The ratio of angular speeds of these two satellites would be 2 : 1.

The ratio of the potential energy of these two satellites would be 1 : 2.

The ratio of the kinetic energies of these two satellites would be 2 : 1.

answer is A, B.

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Detailed Solution

$F = \frac{C}{r} = \frac{m v^{2}}{r}$

$v = same; v = ω_{1} r = ω_{2} \times 2 r$

$\frac{ω_{1}}{ω_{2}} = \frac{2}{1}$

$\frac{dU}{dr} = - \frac{e}{r} \Rightarrow U = - CIn (r)$

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