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  • The radius of a planet is A satellite revolves around it in a circle of radius <img alt="\mathrm{r}"

The radius of a planet is \mathrm{R}.A satellite revolves around it in a circle of radius \mathrm{r} with angular speed \mathrm{\omega}. The acceleration due to gravity on planet's surface will be:
 

Option: 1

\mathrm{\frac{r^3 \omega}{R}}

 


Option: 2

\mathrm{\frac{r^2 \omega^3}{R}}
 


Option: 3

\mathrm{\frac{r^3 \omega^2}{R^2}}
 


Option: 4

\mathrm{\frac{r^2 \omega^2}{R}}


Answers (1)

Let \mathrm{M} be the mass of the planet and \mathrm{m} the mass of satellite. Then

\mathrm{\mathrm{mr} \omega^2=\frac{\mathrm{GMm}}{\mathrm{r}^2} \quad \Rightarrow \quad \mathrm{GM}=\mathrm{r}^3 \omega^2}

\mathrm{\text { Now } g=\frac{\mathrm{GM}}{\mathrm{R}^2}=\frac{\mathrm{r}^3 \omega^2}{\mathrm{R}^2}}

Hence option 3 is correct.




 

Posted by

Kshitij

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