Question

If the radius of the earth were to shrink and its mass were to remain the same, the acceleration due to gravity on the surface of the earth with?

• A. Increase
• B. Decrease
• C. Remains same
• D. Zero

Answer 1

The correct option is A Increase

Gravitational force between two masses = $K\frac{m1m2}{r^2}$

Where

K is universal gravitational constant $m_1$ and $m_2$ are the masses $r$ is the distance between the masses.

Now , the acceleration due to $m1$ being earth will be = $K\frac{m1}{r^2}$

If the radius decreases and the mass remains same the acceleration will increase.