First slide

Motion of planets and satellites

Question

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

Moderate

A

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

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

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

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

Solution

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

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