Question

If the Earth shrinks in its size (radius) mass remaining the same, the value of $g$ on its surface will.

• A. Increase
• B. Decrease
• C. Remains same
• D. Is reduced to zero

Answer 1

Answer: (A)

Increase

Acceleration due to gravity at earth's surface $g=\frac{GM}{R^2}$

where $M$ and $R$ is the mass and radius of earth, respectively.

$⟹$ $g\propto \frac{1}{R^2}$ (for constant $M$)

Hence acceleration due to gravity increases as the radius of earth decreases (i.e if earth shrinks).