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  • A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as on the surface of earth. Its radius in terms of radius of earth <img alt="\m

A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as on the surface of
earth. Its radius in terms of radius of earth \mathrm{R} will be:

Option: 1

\mathrm{R/4}


Option: 2

\mathrm{R/2}


Option: 3

\mathrm{R/3}


Option: 4

\mathrm{R/8}


Answers (1)

best_answer

\mathrm{ g=\frac{G M}{R^2}=\frac{G\left(\frac{4}{3} \pi R^3 \rho\right)}{R^2}=\frac{4}{3} \pi G \rho R }

\mathrm{ \therefore \frac{g_p}{g_e}=\left(\frac{P_p}{P_e}\right)\left(\frac{R_p}{R_e}\right) \Rightarrow 1=(2) \frac{R_p}{R_e} }

\mathrm{ \Rightarrow \frac{R_p}{R_e}=1 / 2 \Rightarrow R_p=\frac{R}{2} }

Hence option 2 is correct.

 

Posted by

sudhir kumar

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