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Question

Two concentric shells of masses $M_{1}$ and $M_{2}$ are having radii $r_{1}$ and $r_{2}$ . Which of the following is the correct expression for the gravitational field at a distance r.

F = \frac{G (M_{1} + M_{2})}{r^{2}} f o r r < r_{1}

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F = \frac{G (M_{1} + M_{2})}{r^{2}} f o r r < r_{2}

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F = \frac{G M_{2}}{r^{2}} f o r r_{1} < r < r_{2}

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F = \frac{G M_{1}}{r^{2}} f o r r_{1} < r < r_{2}

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Solution

The correct option is C $F = \frac{G M_{1}}{r^{2}} f o r r_{1} < r < r_{2}$
For region $r < r_{1}$ , net mass enclosed by the elemental sphere of radius r is zero.
Thus gravitational field is zero for $r < r_{1}$
For region $r_{1} < r < r_{2}$ , net mass enclosed by the elemental sphere of radius r is $M_{1}$ .
Thus gravitational field $F = \frac{G M_{1}}{r^{2}}$ for $r_{1} < r < r_{2}$

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