Physics, asked by Bvss14, 6 months ago

If both the mass and the radius of the earth decreases by 2%, the value of the acceleration due to gravity

Answers

Answered by Anonymous
6

picture :1⬆️⬆️. picture:2⬆️⬆️

Acceleration due to gravity = (1.020408163) g

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see explanation in the attached picture.

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Answered by amitnrw
2

Given : both the mass and the radius of the earth decreases by 2%,

To Find : the value of the acceleration due to gravity

Solution:

g  = GM/R²

mass and the radius of the earth decreases by 2%,  

Using approximation

Mass decreases by 2 %

R² is in denominator  Hence  2² = 4 % increase

Net increase = 2 %

value of the acceleration due to gravity increase by 2 %

if g = 10 m/s²

new acceleration due to gravity = 10.2 m/s²

Exact

g  = GM/R²

=> gₙ   = G (0.98M)/(0.98R)²

=> gₙ = GM/0.98R²

=> gₙ =1.02041 (GM/R²)

Hence increase by  2.041 %

if g = 10 m/s²

new acceleration due to gravity = 10.2041  m/s²

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