Question

The mass of the planet is $ \frac{1}{9} $ th of the mass of the earth and its radius is half that of the earth. If a body weighs 450 N on the earth, then it is weight on the planet would be:

• A. 100 N
• B. 200 N
• C. 450 N
• D. 900 N

Answer 1

Answer: (B)

Here: mass of planet $ {{M}_{p}}=\frac{{{M}_{e}}}{9} $ where $ {{M}_{e}} $ mass of earth is. weight of the body on earth $ {{w}_{e}}=450\,N $ radius of the planet $ {{R}_{p}}=\frac{{{R}_{e}}}{2} $ (where $ {{R}_{e}} $ is radius of earth) From the law of gravitation that weight of the body $ w=\frac{GMm}{{{R}^{2}}}\Rightarrow w\propto \frac{M}{{{R}^{2}}} $ Hence, $ \frac{{{w}_{e}}}{{{w}_{p}}}=\frac{{{M}_{e}}}{{{M}_{p}}}\times {{\left( \frac{{{R}_{p}}}{{{R}_{e}}} \right)}^{2}} $ or $ \frac{450}{{{w}_{p}}}=\frac{{{M}_{e}}}{\left( \frac{{{M}_{e}}}{9} \right)}\times \frac{{{\left( \frac{{{R}_{e}}}{2} \right)}^{2}}}{R_{e}^{2}} $ so, $ {{w}_{p}}=\frac{450\times 4}{9}=200N $