Question

The mass of a planet is 1/9 of the mass of the earth and its radius is half that of the earth. If a body weights 9 N on the earth, its weight on the planet would be:

• A. 6 N
• B. 4 N
• C. 2.25 N
• D. I N

Answer 1

Answer: (B)

Weight of the object of mass m on earth $W_e=m{g}_e=\frac{G{M}_{e}m}{R_e^2}$ ?(i) Weight of object of mass m on planet $W_p=m{g}_p=\frac{G{M}_{p}m}{R_p^2}$ ?(ii) From Eqs. (i) and (ii) $\frac{W_p}{W_e}=\frac{G{M}_{p}m}{r_p^2}\times \frac{R_e^2}{G{M}_{e}m}$ $=\frac{M_p}{M_e}{\left(\frac{R_e}{R_p}\right)}^2$ ?(iii) $\left(\begin{array}{rl}& \text{Given: }{M}_p=\frac{1}{9}{m}_e\\ & r_p=\frac{1}{2}{R}_e\\ & W_e=9N\end{array}\right)$ $\frac{W_p}{W_e}=\frac{\frac{1}{9}{M}_e}{M_e}\times {\left(\frac{R_e}{1/2R_e}\right)}^2$ $W_p=\frac{4}{9}\times 9=4N$