JEE Main 2025 Jan 24 Shift 2, Physics Q25: Variation In Acceleration Due To Gravity

JEE Main2025Jan 24, Shift 2Physics

Acceleration due to gravity on the surface of earth is ' $g$ '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ______ $g$ .

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Solution

Acceleration due to gravity at the surface:

$g = \frac{G M _{e}}{R _{e}^{2}}$

If the diameter (and hence the radius) is reduced to $\frac{1}{3}$ while the mass is held constant, the new value is:

$g^{'} = \frac{G M _{e}}{( R _{e} /3 ) ^{2}} = \frac{G M _{e}}{R _{e}^{2} /9} = 9 \cdot \frac{G M _{e}}{R _{e}^{2}} = 9 g$

Answer: 9

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JEE Main 2025 Jan 24 Shift 2, Physics Q25: Variation In Acceleration Due To Gravity

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