Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

Dependence of intensity of gravitational field ( $E$ ) of the earth with distance ( $r$ ) from the centre of the earth is correctly represented by: (where $R$ is the radius of the earth)

Option 1

Option 2

Option 3

Option 4

Step-by-Step Solution

Field Inside the Earth ( $r < R$ ): Assuming the Earth is a solid sphere of uniform density, the acceleration due to gravity (gravitational field intensity) at a depth $d$ is given by $g(d) = \frac{GM}{R^3}(R-d)$ [Equation 7.19]. Since the distance from the center is $r = R-d$ , this becomes $g(r) = \frac{GM}{R^3}r$ . Thus, $E \propto r$ (Linear increase passing through the origin).
Field Outside the Earth ( $r > R$ ): For points outside the Earth, the field behaves as if the entire mass is concentrated at the center. The formula is $g(r) = \frac{GM}{r^2}$ [Equation 7.13 derived]. Thus, $E \propto \frac{1}{r^2}$ (Rectangular hyperbola decreasing with distance).
At the Surface ( $r = R$ ): The field reaches its maximum value.
Graphical Representation: The correct graph shows a straight line rising from the origin to $r=R$ , followed by a curve decreasing as $1/r^2$ for $r > R$ . This corresponds to the standard graphical representation for this problem (typically Option 1 in this PYQ).

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