Question

If the radius of the earth shrinks by 2% while its mass remains the same. The acceleration due to gravity on the earth's surface will approximately ______.

Options

• decrease by 2%

• decrease by 4%

• increase by 2%

• increase by 4%

Answer 1

If the radius of the earth shrinks by 2% while its mass remains the same. The acceleration due to gravity on the earth's surface will approximately increase by 4%.

Explanation:

Relation between acceleration due to gravity (g) and radius of the earth (R), g = `(GM)/R^2`

M = constant, g = `1/R^2`

`100 xx (Deltag)/g = -2(DeltaR)/R xx 100`

% change in g = -2(-2) = 4%

So acceleration due to gravity on the earth's surface will increase by 4%.