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if the radius of the earth sinks by 1% and its density remain constant then what is the change in value of acceleration due to gravity of earth at its surface. Please solve it by using error concept, I have a little confusion in it.
Asked by srkgb8018 | 15 May, 2024, 08:12: PM
answered-by-expert Expert Answer

Acceleration due to gravity g = G ( M / R2 )

where G is universal gravitational constant , M is mass of earth and R is radius of earth.

If consider earth as sphere of radius R and ρ is its density , then

Mass M = volume × density = (4/3) π R3 × ρ

Hence , acceleration due to gravity g = G [  (4/3) π R3 × ρ ] / R2 = ( G (4/3) π  ρ ) R

Hence , acceleration due to gravity of earth is directly proportional to radius of earth .

Hence if radius decreases by 1% , then acceleration due to gravity is also decreases by 1 %

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