Question

The ratio of an angular velocity of two satellites revolving around the planet is $2:3$. Calculate the ratio of the distance between the satellites and center of the planet.

• A. $3\sqrt{\frac{6}{17}}$
• B. $\sqrt{\frac{17}{18}}$
• C. $3\sqrt{\frac{16}{9}}$
• D. $3\sqrt{\frac{9}{4}}$

Answer 1

The correct option is D $3\sqrt{\frac{9}{4}}$

$T^2\alpha R^3\Rightarrow {\left(\frac{2\pi }{w}\right)}^2\alpha R^3\Rightarrow \frac{1}{w^2}\alpha R^3\therefore \frac{{w_2}^2}{{w_1}^2}=\frac{{R_1}^3}{{R_1}^3}$

Given that, $\Rightarrow \frac{w_2}{w_1}=\frac{2}{3}\Rightarrow {\left(\frac{3}{2}\right)}^2={\left(\frac{R_1}{R_2}\right)}^2$

$\Rightarrow \frac{R_1}{R_2}=3\sqrt[]{\frac{9}{4}}$