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7.Gravitation
normal
The orbital velocity of an artificial satellite in a circular orbit very close to earth is $v$. The velocity of a geo-stationary satellite orbiting in circular orbit at an altitude of $3R$ from earth's surface will be
A
$\frac{v}{{\sqrt 7 }}$
B
$\frac{v}{{\sqrt 6 }}$
C
$\frac{v}{2}$
D
$\frac{v}{{\sqrt 2 }}$
Solution
$\mathrm{v}_{0}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \Rightarrow \mathrm{v}_{0} \propto \frac{1}{\sqrt{\mathrm{r}}}$
$\Rightarrow \frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=\sqrt{\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}} \Rightarrow \quad \frac{\mathrm{v}}{\mathrm{v}_{2}}=\sqrt{\frac{4 \mathrm{R}}{\mathrm{R}}} ; \mathrm{v}_{2}=\frac{\mathrm{v}}{2}$
Standard 11
Physics
