What would be the change in acceleration due to gravity (g) at the surface, if the radius of earth decreases by 2% keeping the mass of earth constant?
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Answered by
5
The acceleration would increase by 4%
Answered by
14
Hey mate,
◆ Answer -
g will increase by 4%.
◆ Explanation-
# Given-
R' = 98% R
M = constant
# Formula-
Gravitational acceleration due to earth is given by-
g = GM/R^2
When radius is decreased by 2% keeping mass constant,
g' = GM/R'^2
g' = GM/(98%R)^2
Taking ratio-
g'/g = [GM/(98%R)^2] / [GM/R^2]
g'/g = (100/98)^2
g'/g = 104.12%
Thus, gravitational acceleration will increase by approximately 4%.
Hope that was useful...
◆ Answer -
g will increase by 4%.
◆ Explanation-
# Given-
R' = 98% R
M = constant
# Formula-
Gravitational acceleration due to earth is given by-
g = GM/R^2
When radius is decreased by 2% keeping mass constant,
g' = GM/R'^2
g' = GM/(98%R)^2
Taking ratio-
g'/g = [GM/(98%R)^2] / [GM/R^2]
g'/g = (100/98)^2
g'/g = 104.12%
Thus, gravitational acceleration will increase by approximately 4%.
Hope that was useful...
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