Question

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:

• A. g/4
• B. 4g
• C. g/2
• D. 2g

Answer 1

Answer: (B)

4g

Answer 2

The acceleration due to gravity on the surface of the earth is given by:

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

where $G$ is the gravitational constant, $M$ is the mass of the earth, and $R$ is the radius of the earth.

If the diameter of the earth is reduced to half, the radius $R$ will also be reduced to half, becoming $\frac{R}{2}$. Substituting $R' = \frac{R}{2}$ into the formula for $g$, we get:

$g' = \frac{GM}{(R/2)^2} = \frac{GM}{R^2/4} = 4 \cdot \frac{GM}{R^2} = 4g$
Thus, the new acceleration due to gravity on the surface of the earth would be $4g$.