Question

If radius of earth shrinks by $1$ when mass remains same, the acceleration due to gravity on the surface of earth would

• A. remain unchanged
• B. decrease by 2%
• C. become zero
• D. increase by 2%.

Answer 1

Answer: (B)

decrease by 2%

Answer 2

$g = \frac{GM}{R^2}$ Here $g \propto \frac{1}{R^2}$ and $g' \propto \frac{1}{(0.99R)^2} \propto \frac{0.98}{R^2}$ i.e. $\frac{g'}{g}$ = 0.98 i.e. g' = 0.98 g Clearly g' decreases by 2%.