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Two planets A and B of radii R and 1.5 R have densities \rho and \frac{\rho}{2} respectively. The ratio of acceleration due to gravity at the surface of B to A is :

Option: 1

2 : 3 


Option: 2

2 : 1 


Option: 3

4 : 3 


Option: 4

3 : 4


Answers (1)

best_answer

\begin{aligned} & \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}=\frac{\mathrm{G} \times \frac{4}{3} \pi \mathrm{R}^3 \times \rho}{\mathrm{R}^2}=\frac{4}{3} \mathrm{G} \pi \mathrm{PR} \\ & \frac{\mathrm{g}_2}{\mathrm{~g}_1}=\frac{\mathrm{R}_2}{\mathrm{R}_1} \times \frac{\rho_2}{\rho_1}=1.5 \times \frac{1}{2}=\frac{3}{4} \end{aligned}

Posted by

Gautam harsolia

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