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Two identical spheres of gold are in contact with each other. The gravitational force of attraction between them is

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directly proportional to the square of their radius

directly proportional to the cube of their radius

directly proportional to the fourth power of their radius

inversely proportional to the square of their radius.

answer is C.

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Detailed Solution

F = GM₁M₂ / r²

Here M₁ = M₂ = 4/3 π R³ .d

and r = R + R = 2R

Where R = radius of each sphere

and r = distance between their centres

$∴ F = \frac{G \cdot {(\frac{4}{3} π R^{3} d)}^{2}}{4 R^{2}}$

$\Rightarrow F \propto R^{4}$

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