Question

If radius of the were to shrink by $1\%,$ It's mass remain same the the value of g on the earth

surface would

• A. increase by $0.5\%$
• B. decrease by $0.5\%$
• C. increase by $2\%$
• D. decrease by $2\%$

Answer 1

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

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

$\frac{dg}{g}=-2\frac{dR}{R}$

$given\frac{dR}{R}=-1\%$

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

$\therefore gincreasesby2\%$

Hence,

option $C$ is correct answer.