First slide

Gravitational field intensity

Question

Two concentric shells of masses M₁ and M₂, are . having radii r₁, andr₂. Which of the following is correct expression for the gravitational field on a mass m?

Moderate

A

$F = \frac{G (M_{1} + M_{2})}{r^{2}}, for r < r_{1}$
B

$F = \frac{G (M_{1} + M_{2})}{r^{2}}, for r < r_{2}$
C

$F = \frac{{GM}_{2}}{r^{2}}, for r_{1} < r < r_{2}$
D

$F = \frac{G^{2}}{r^{2}}, for r_{1} < r < r_{2}$

Solution

We know that the gravitational field in aside a shell is zero but for points outside it, the shell behaves as if whole of its mass is concentrated at its centre. When a point lies in between the shells $(r_{1} < r < r_{2})$ , there will be field due to inner shell only. The gravitational field is given by
$F = ({GM}_{1} / r^{2})$
The gravitational field due to outer shell will be zero because the point lies within the shell

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