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  • A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:Opti

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing
W on earth will weigh on that planet:

Option: 1

2^{\frac{1}{3}} \mathrm{W}


Option: 2

2W


Option: 3

W


Option: 4

2^{\frac{2}{3}} \mathrm{W}


Answers (1)

best_answer

Average Density of planet = average density of earth

 

\begin{aligned} & \frac{M_e}{\frac{4}{3} \pi R_e^3}=\frac{M_p}{\frac{4}{3} \pi R_p^3} \\ & \Rightarrow \frac{M_e}{R_e^3}=\frac{2 M_e}{R_p^3} \\ & \Rightarrow R_p=2^{\frac{1}{3}} R_e--\cdots---(i) \\ & \text { Now, } g=\frac{G M}{R^2} \\ & \frac{g_e}{g_p}=\frac{M_e}{R_e^2} \times \frac{R_p^2}{2 M_e}=2^{\frac{2}{3}-1}=2^{-\frac{1}{3}} \\ & \Rightarrow g_p=2^{\frac{1}{3}} g_e \\ & \Rightarrow W_p=2^{\frac{1}{3}} W_e \end{aligned}

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