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7.Gravitation
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A satellite is orbitting around the earth with areal speed $v_a$. At what height from the surface of the earth, it is rotating, if the radius of earth is $R$
A
$\frac{{4v_a^2}}{{g{R^2}}} - R$
B
$\frac{{2v_a^2}}{{g{R^2}}} - R$
C
$\frac{{v_a^2}}{{g{R^2}}} - R$
D
$\frac{{v_a^2}}{{2g{R^2}}} - R$
Solution
$v_{a}=\frac{d A}{d t}=\frac{1}{2} r v \Rightarrow v_{a}^{2}=\frac{1}{4} r^{2} v^{2}$
$\Rightarrow v_{a}^{2}=\frac{1}{4} r^{2} \times \frac{g R^{2}}{r}$
$\mathrm{r}=\frac{4 \mathrm{v}_{\mathrm{a}}^{2}}{\mathrm{g} \mathrm{R}^{2}} \quad \therefore \mathrm{h}=\frac{4 \mathrm{v}_{\mathrm{a}}^{2}}{\mathrm{g} \mathrm{R}^{2}}-\mathrm{R}$
Standard 11
Physics
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