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 formula for acceleration due to gravity \( g \) is:\n\[\ng = \frac{GM}{R^2}\n\]\nWhere:\n- \( G \) is the gravitational constant\n- \( M \) is the Earth's mass\n- \( R \) is the Earth's radius\n\nIf the Earth's radius shrinks by 4% to \( 0.96R \), the new acceleration is:\n\[\ng' = \frac{GM}{(0.96R)^2} = \frac{GM}{0.9216 R^2} = \frac{g}{0.9216}\n\]\nThus, the percentage change in \( g \) is:\n\[\n\frac{1 - 0.9216}{0.9216} \times 100 \approx 16\%\n\]\nTherefore, the answer is 16%.