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  • Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :Option: 1 2W

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :
Option: 1 2W      
Option: 2 W
Option: 3 2^{\frac{1}{3}}W
Option: 4 \sqrt{2}W

Answers (1)

best_answer

m_{planet}= 2m_{earth}
\rho_{planet}= \rho_{earth}
As,W= mg,
W_{planet}= mg_{p}
W_{earth}= mg_{e}
m\rightarrow mass\, of\, the\, body
\frac{W_{planet}}{W_{earth}}= \frac{W_{p}}{W}= \frac{g_{p}}{g_{e}}= \frac{\frac{GM_{p}}{R^{2}_{p}}}{\frac{GM_{e}}{R^{2}_{e}}}
\frac{W_{p}}{W}=\frac{\rho_{p}\times R_{p}}{\rho_{e}\times R_{e}}= \frac{R_{p}}{R_{e}}
\because m_{p}= 2m_{e}
\rho_{p}\times R_{p}^{3}= 2\times \rho_{e}\times R_{e}^{3}
\frac{R_{p}}{R_{e}}= 2^{\frac{1}{2}}
\therefore \frac{W_{p}}{W}= 2^{\frac{1}{3}}
W_{p}= 2^{\frac{1}{2}}W
The correct option is (3)
 

Posted by

vishal kumar

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