Question

If the radius of Earth shrinks by 4% and mass of Earth unchanged, then the value of acceleration due to gravity will be changed by:

• A. 16%
• B. 8%
• C. 2%
• D. 4%

Hint:

When the radius of Earth changes, the acceleration due to gravity changes with the square of the radius, so a 4% shrinkage in radius results in a 16% increase in gravity.

Answer 1

The Correct Option is A

The acceleration due to gravity \( g \) is given by the formula: \[ g = \frac{GM}{R^2} \] Where: - \( G \) is the gravitational constant - \( M \) is the mass of the Earth - \( R \) is the radius of the Earth Since the mass of the Earth remains unchanged and the radius shrinks by 4%, the new radius is \( 0.96R \). The new acceleration due to gravity is: \[ g' = \frac{GM}{(0.96R)^2} = \frac{GM}{0.9216 R^2} = \frac{g}{0.9216} \] Thus, the percentage change in \( g \) is: \[ \frac{1 - 0.9216}{0.9216} \times 100 \approx 16\% \] Therefore, the correct answer is 16%.