Question

If the radius of the earth were to shrink by $1\%$ its mass remaining the same, the acceleration due to gravity on the earths surface would

• A. decrease by $2\%$
• B. remain unchanged
• C. increase by $2\%$
• D. will increase by $9.8\%$

Answer 1

The correct option is C increase by $2\%$

The expression for g is given by

$g=\frac{GM}{R^2}$

$\frac{dg}{g}=\frac{2dR}{R}=2\times 1\%$

$\frac{dg}{g}=2\%$