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Question Number 171359 by Mr.D.N. last updated on 13/Jun/22

$$\mathrm{A}\mathrm{heavenly}\mathrm{body}\mathrm{has}\mathrm{mass}\mathrm{one}\mathrm{third}\mathrm{of}\mathrm{the}\mathrm{earth}\mathrm{and}\mathrm{its}$$$$\mathrm{radius}\mathrm{is}\mathrm{half}\mathrm{as}\mathrm{that}\mathrm{of}\mathrm{the}\mathrm{earth}.\mathrm{if}\mathrm{a}\mathrm{stone}\mathrm{weights}200\mathrm{N}\mathrm{on}$$$$\mathrm{the}{\mathrm{earth}}^{\prime }\mathrm{s}\mathrm{surface},\mathrm{find}\mathrm{its}\mathrm{weight}\mathrm{on}\mathrm{that}\mathrm{heavenly}\mathrm{body}.$$

Answered by aleks041103 last updated on 13/Jun/22

$$W=\frac{{GM}_{pl}m}{R^2}\sim \frac{M}{R^2}$$$$\Rightarrow \frac{W_{earth}}{W_{planet}}=\frac{M_{earth}}{M_{pl}}{\left(\frac{R_{pl}}{R_{earth}}\right)}^2=\frac{1}{\frac{1}{3}}{\left(\frac{1}{2}\right)}^2=\frac{3}{4}$$$$\Rightarrow W_{pl}=\frac{4}{3}{W}_{earth}\approx 266.7N$$

Commented by Mr.D.N. last updated on 14/Jun/22

$$\mathrm{great}\mathrm{thank}\mathrm{you}.$$

Commented by peter frank last updated on 23/Jun/22

$$\mathrm{thank}\mathrm{s}$$

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