Question

If the radius of earth shrinks by one percent and its mass remaining the same, then acceleration due to gravity on the earth?s surface will

• A. remain constant
• B. decrease
• C. increase
• D. either (b) or (c)

Answer 1

Answer: (C)

increase

Answer 2

Acceleration due to gravity on the earth's surface is given by $g=\frac{G M_{e}}{R_{e}^{2}}$ Now, $R_{e}$ shrinks by $1 \%$, so the new value for radius of the earth is $0.09\, R_{e}$. $\therefore\,\,\,\, g'=\frac{G M_{e}}{(0.09)^{2} R_{e}^{2}}=\frac{g}{0.0081} > g$