Question

If the Earth shrinks in its radius by 4%, mass remaining the same, the value of 'g' on its surface

• A. decreases by about 4%
• B. increases by about 8%
• C. decreases by about 8%
• D. remains constant

Answer 1

Answer: (B)

increases by about 8%

Answer 2

We know, $g = \frac{GM}{R^2}$
Since G and M are constants, so g increases as R decreases
$\frac{\Delta g}{g} = \frac{\Delta R}{R}$
As $\frac{\Delta R}{R} =4\%$
So, $\frac{\Delta g}{g} = 8\%$