Question

If the mass of the earth is $ 80 $ times of that of planet and diameter is double that of planet and $ g $ on earth $ 9.8\,\,m/{{s}^{2}} $ . Then, the value of $ g $ on the planet will be

• A. $ 0.49\,\,m/{{s}^{2}} $
• B. $ 4.9\,\,m/{{s}^{2}} $
• C. $ 0.98\,\,m/{{s}^{2}} $
• D. $ 9.8\,\,m/{{s}^{2}} $

Answer 1

Answer: (A)

Mass of the earth $ {{M}_{e}}=80\,\,{{M}_{p}} $ Diameter of earth $ {{D}_{e}}=2\,\,{{D}_{p}} $ or radius of the earth $ {{R}_{e}}=2\,\,{{R}_{p}} $ Gravitational acceleration is $ g=\frac{GM}{{{R}^{2}}}\propto \frac{M}{{{R}^{2}}} $ or $ \frac{{{g}_{e}}}{{{g}_{p}}}=\frac{{{M}_{e}}}{{{M}_{p}}}\times {{\left( \frac{{{R}_{p}}}{{{R}_{e}}} \right)}^{2}} $ $ \frac{{{g}_{e}}}{{{g}_{p}}}=\frac{80\,{{M}_{p}}}{{{M}_{p}}}\times {{\left( \frac{{{R}_{p}}}{2{{R}_{p}}} \right)}^{2}}=80\times \frac{1}{4}=20 $ So, $ {{g}_{p}}=\frac{{{g}_{e}}}{20}=\frac{9.8}{20}=0.49\,\,m/{{s}^{2}} $