Question

If the radius of the earth were to shrink by one percent, its mass remaining the same, the value of \( g \) on the earth’s surface would:

• A. increase by 0.5%
• B. increase by 2%
• C. decrease by 0.5%
• D. decrease by 2%

Hint:

Gravity on the surface of a planet increases if its radius decreases, even if its mass remains constant.

Answer 1

The Correct Option is B

Step 1: Gravitational force relation.
The acceleration due to gravity \( g \) 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.

Step 2: Effect of change in radius.
If the radius \( R \) decreases by 1%, then \( g \) will increase, as gravity is inversely proportional to the square of the radius. The percentage increase in \( g \) is approximately 2%.
Thus, the correct answer is (2).