JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Gravitation

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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.

Answer: 9

Solution

Surface gravity is

g = \frac{GM}{R ^{2}}

, where

R

is the Earth's radius and

M

its mass.

If the diameter is reduced to one-third of its original value while the mass is unchanged, the radius also becomes

R /3

. The new surface gravity is

g^{'} = \frac{GM}{( R /3 ) ^{2}} = \frac{9 GM}{R ^{2}} = 9 g .

The new acceleration due to gravity is

9 g

, so the required integer is

9

JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Integer answer

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