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 $w_e=450N$ 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, $w_p=\frac{450\times 4}{9}=200N$