Question

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

• A. decreases by $19$%
• B. increases by $19$%
• C. decreases by $23$%
• D. increases by $23$%

Answer 1

The correct option is D increases by $23$%

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

Given that, $M\to M$

$R\to 0.9R$

$\therefore g^{\prime }=\frac{GM}{(0.9R{)}^2}=\frac{GM}{0.81R^2}=\frac{9}{0.81}=1.3g$

$\therefore$ Percentage increase=$\frac{g^{\prime }-g}{g}\times 100=23\%$