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If orbital velocity of planet is given by $v = G^{a} M^{b} R^{c}$ , then

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$a = 1 / 2, b = - 1 / 2, c = - 1 / 2$

$a = 1 / 2, b = 1 / 2, c = - 1 / 2$

$a = 1 / 3, b = 1 / 3, c = - 1 / 3$

$a = 1 / 2, b = - 1 / 2, c = 1 / 2$

answer is B.

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Detailed Solution

$v = \sqrt{\frac{GM}{R}} = G^{1 / 2} M^{1 / 2} R^{- 1 / 2}$

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