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(B) The orbital velocity $v_0$ of a satellite revolving around the earth at a distance $r$ from the center is given by the formula:$v_0 = \sqrt{\frac{

Vedclass · Accepted Answer

$4/3$

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(B) The orbital velocity $v_0$ of a satellite revolving around the earth at a distance $r$ from the center is given by the formula:$v_0 = \sqrt{\frac{GM}{r}}$From this expression,it is clear that the orbital velocity is inversely proportional to the square root of the orbital radius:$v_0 \propto \frac{1}{\sqrt{r}}$Given the radii of the two satellites are $r_1 = 9R$ and $r_2 = 16R$,the ratio of their speeds $v_1$ and $v_2$ is:$\frac{v_1}{v_2} = \sqrt{\frac{r_2}{r_1}}$Substituting the given values:$\frac{v_1}{v_2} = \sqrt{\frac{16R}{9R}} = \sqrt{\frac{16}{9}} = \frac{4}{3}$Therefore,the ratio of the speeds is $4/3$.

Two satellites of mass $50\,kg$ and $100\,kg$ revolve around the earth in circular orbits of radius $9\,R$ and $16\,R$ respectively,where $R$ is the radius of the earth. The ratio of the speeds of the two satellites will be:

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