Question

If the radius of earth is decreased by $4$% and its density remains same, then escape velocity from its surface will-

• A. remain same
• B. increases by $9$%
• C. decrease by $4$%
• D. increase by $2$%

Answer 1

The correct option is B increases by $9$%

Acceleration due to gravity at surface of the earth is $g=\frac{GM}{R^2}$

Radius of earth decreases by $4$%

therefore $R^1=R-0.04R=0.96R$

Acceleration due to gravity

$g^1=\frac{GM}{{\left(0.96R\right)}^2}=1.09g$

Percentage increase in acceleration due to gravity $\frac{g^1-g}{g}\times 100=9$%

Increase by $9$%