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

The Correct Option is A

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.