1. Tardigrade
  2. Question
  3. Physics
  4. 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:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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:

EAMCETEAMCET 1997

Solution:

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{align} & \text{Given: }{{M}_{p}}=\frac{1}{9}{{m}_{e}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{r}_{p}}=\frac{1}{2}{{R}_{e}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{W}_{e}}=9N \\ \end{align} \right) $ $ \frac{{{W}_{p}}}{{{W}_{e}}}=\frac{\frac{1}{9}{{M}_{e}}}{{{M}_{e}}}\times {{\left( \frac{{{R}_{e}}}{1/2{{R}_{e}}} \right)}^{2}} $ $ {{W}_{p}}=\frac{4}{9}\times 9=4N $