A uniform sphere has radius ' R ' and mass ' M '. The magnitude of gravitational field at distances ' r₁ ' and ' r₂ ' from the centre of the sphere are ' E₁ ' and ' E₂ ' respectively. The ratio E₁: E₂ is ( r₁ > R and r₂ < R) (a) (R²)/(r₁² r₂) (b) (R³)/(r₁ r₂) (c) (R³)/(r₁² r₂) (d) (R³)/(r₁ r₂²)

Answer: (c). Outside ( r₁ > R): E₁ = (GM)/(r₁²). Inside ( r₂ < R): E₂ = (GMr₂)/(R³). E₁: E₂ = (R³)/(r₁² r₂) So the answer is (c) (R³)/(r₁² r₂).

A uniform sphere has radius ' R ' and mass ' M '. The magnitude of… | MHT CET 2025 (5 May, Shift 2)

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Gravitational Field

A uniform sphere has radius ' $R$ ' and mass ' $M$ '. The magnitude of gravitational field at distances ' $r_1$ ' and ' $r_2$ ' from the centre of the sphere are ' $E_1$ ' and ' $E_2$ ' respectively. The ratio $E_1 : E_2$ is ( $r_1 > R$ and $r_2 < R$ )

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Answer: (c)

Outside ( $r_1 > R$ ): $E_1 = \frac{GM}{r_1^2}$ .
Inside ( $r_2 < R$ ): $E_2 = \frac{GMr_2}{R^3}$ .
$E_1 : E_2 = \frac{R^3}{r_1^2 r_2}$
So the answer is (c) $\frac{R^3}{r_1^2 r_2}$ .

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Gravitational Field question from MHT CET 2025 (5 May, Shift 2)

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