Question

The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in ratio

• A. 1 : 2
• B. 2 : 3
• C. 2 : 1
• D. 4 : 1

Answer 1

Answer: (C)

The gravity $ g=\frac{4}{3}G\pi R\rho $ The ratio of gravities on the planet $ \frac{{{g}_{1}}}{{{g}_{2}}}=\frac{{{\rho }_{1}}{{R}_{1}}}{{{\rho }_{2}}{{R}_{2}}} $ $ \frac{{{g}_{1}}}{{{g}_{2}}}=\frac{1}{2}\times \frac{4}{1}=\frac{2}{1} $