Two identical metal spheres are kept in contact with each other, each having radius ' R ' cm and ' ρ ' is the density of material of metal spheres. The gravitational force ' F ' of attraction between them is proportional to (a) R³ρ (b) R⁴ρ² (c) R⁴ρ (d) R³ρ²

Answer: (b). Each mass M = 4/3π R³ρ; centres in contact are 2R apart. F = (GM²)/((2R)²) = G/4R²(4/3π R³ρ)² ∝ R⁴ρ² So the answer is (b) R⁴ρ².

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Newton's Law of Gravitation

Two identical metal spheres are kept in contact with each other, each having radius ' $R$ ' cm and ' $\rho$ ' is the density of material of metal spheres. The gravitational force ' $F$ ' of attraction between them is proportional to

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Answer: (b)

Each mass $M = \frac{4}{3}\pi R^3\rho$ ; centres in contact are $2R$ apart.
$F = \frac{GM^2}{(2R)^2} = \frac{G}{4R^2}\left(\frac{4}{3}\pi R^3\rho\right)^2 \propto R^4\rho^2$
So the answer is (b) $R^4\rho^2$ .

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Newton's Law of Gravitation question from MHT CET 2024 (3 May, Shift 2)

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