First slide

Gravitational force and laws

Question

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. $F \propto 1 / r^{3}$ , but still remaining a central force. Then

Moderate

A

Kepler's law of areas still holds
B

Kepler's law of period still holds
C

Kepler's law of areas and period still hold
D

Neither the law of areas, nor the law of period still holds

Solution

$F = \frac{G M m}{r^{3}} \frac{m v^{2}}{r} = \frac{G M m}{r^{3}} v = \sqrt{\frac{G M}{r^{2}}} = \frac{\sqrt{G M}}{r} T = \frac{2 πr}{V} = \frac{2 πr}{\frac{\sqrt{GM}}{r}} = \frac{2 {πr}^{2}}{\sqrt{GM}} T^{2} = \frac{4 π^{2} r^{4}}{GM}$
Both the kepler laws does not hold good

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