Question

If the radius of earth is reduced by 1% without changing the mass, then change in the acceleration due to gravity will be:

• A. 2% decrease
• B. 2% increase
• C. 1% increase
• D. 1% decrease

Answer 1

Answer: (A)

2% decrease

Answer 2

Here: ${{R}_{1}}=R$ (initial radius) ${{R}_{2}}=R\,(1-0.01)$ (final radius) $=0.99R$ Acceleration due to g $g=\frac{GM}{{{R}^{2}}}\propto \frac{1}{{{R}^{2}}}$ Hence, $\frac{{{g}_{1}}}{{{g}_{2}}}={{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}={{\left( \frac{0.99R}{R} \right)}^{2}}=0.98$ or, ${{g}_{2}}=\frac{{{g}_{1}}}{0.98}=1.02{{g}_{1}}$ Hence change in gravitational acceleration $={{g}_{2}}-{{g}_{1}}=1.02{{g}_{1}}-{{g}_{1}}=0.02{{g}_{1}}=2$ positive sign indicates increment.