Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

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).

Option 1

Option 2

Option 3

Option 4

Step-by-Step Solution

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 $0 \le r < R$ , $E = 0$ .
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: $E = \frac{GM}{r^2}$ .
At the Surface ( $r = R$ ): The field is maximum, $E = \frac{GM}{R^2}$ .
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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