The magnitude of gravitational field at distance ' r₁ ' and ' r₂ ' from the centre of a uniform sphere of radius ' R ' and mass ' M ' are ' F₁ ' and ' F₂ ' respectively. The ratio ' (F₁/F₂) ' will be (if r₁ > R and r₂ < R) (a) (R²)/(r₁ r₂) (b) (R³)/(r₁ r₂²) (c) (R³)/(r₁² r₂) (d) (R⁴)/(r₁² r₂²)

Answer: (c). Outside ( r₁ > R): F₁ = (GM)/(r₁²). Inside ( r₂ < R): F₂ = (GMr₂)/(R³). (F₁)/(F₂) = (R³)/(r₁² r₂) So the answer is (c) (R³)/(r₁² r₂).

The magnitude of gravitational field at distance ' r₁ ' and ' r₂ '… | MHT CET 2024 (2 May, Shift 1)

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Gravitational Field

The magnitude of gravitational field at distance ' $r_1$ ' and ' $r_2$ ' from the centre of a uniform sphere of radius ' $R$ ' and mass ' $M$ ' are ' $F_1$ ' and ' $F_2$ ' respectively. The ratio ' $(F_1/F_2)$ ' will be (if $r_1 > R$ and $r_2 < R$ )

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Answer: (c)

Outside ( $r_1 > R$ ): $F_1 = \frac{GM}{r_1^2}$ .
Inside ( $r_2 < R$ ): $F_2 = \frac{GMr_2}{R^3}$ .
$\frac{F_1}{F_2} = \frac{R^3}{r_1^2 r_2}$
So the answer is (c) $\frac{R^3}{r_1^2 r_2}$ .

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Gravitational Field question from MHT CET 2024 (2 May, Shift 1)

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