Question

If the radius of the earth decreases by 10%, the mass remaining unchanged, then acceleration due to gravity will

• A. decreases by 19 %
• B. increases by 19 %
• C. decreases by more than 19 %
• D. increases by more than 19 %

Answer 1

The correct option is D increases by more than 19 %

Acceleration due to gravity
$g=\frac{GM}{R^2}$

as given, radius is decreased by $10$ %.
so $R^{\prime }=0.9R$

Now, new acceleration due to gravity $g^{\prime }=\frac{GM}{(0.9R{)}^2}$

$\frac{g^{\prime }}{g}=\frac{\frac{GM}{(0.9R{)}^2}}{\frac{GM}{R^2}}\frac{g^{\prime }}{g}=\frac{1}{0.81}{g}^{\prime }=1.23g$

So acceleration due to gravity is increased by 23%.

Hence, option D is correct.