Which one of the following plots represent the variation of gravitational field on a particle at distance $r$,

Question

Which one of the following plots represent the variation of gravitational field on a particle at distance $r$, due to a thin spherical shell of radius $R$? ($r$ is measured from the centre of the spherical shell).

Accepted Answer

1. **Gravitational Field Inside a Shell ($r < R$):** According to Newton's shell theorem, the force of attraction (and thus the gravitational field $E$ or $g$) on a point mass situated inside a thin spherical shell of uniform density is zero at all points. Thus, for $0 \le r < R$, $E = 0$.
2. **Gravitational Field Outside a Shell ($r \ge R$):** For a point situated outside the shell, the gravitational force is the same as if the entire mass $M$ of the shell were concentrated at its centre. Thus, the field follows the inverse square law: $E = \frac{GM}{r^2}$.
3. **At the Surface ($r = R$):** The field is maximum, $E = \frac{GM}{R^2}$.
4. **Graphical Representation:** The correct plot must show $E=0$ for $r < R$. At $r=R$, the graph jumps discontinuously to a maximum value and then decreases as $1/r^2$ for $r > R$. This specific shape (zero then a sharp rise followed by a hyperbolic decay) corresponds to Option 2 in the standard set of graphs for this problem.

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