If both the mass and the radius of the earth decreases by 2%, the value of the acceleration due to gravity
Answers
picture :1⬆️⬆️. picture:2⬆️⬆️
Acceleration due to gravity = (1.020408163) g
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see explanation in the attached picture.
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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