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  • A satellite is launched in the equatorial plane in such a way that it can transmit signals upto 600 latitude on the earth. The angular velocity of the satellite is :<div class='qna-o

A satellite is launched in the equatorial plane in such a way that it can transmit signals upto 600 latitude on the earth. The angular velocity of the satellite is :

Option: 1

\sqrt{\frac{GM}{8R^{3}}}


Option: 2

\sqrt{\frac{GM}{2R^{3}}}


Option: 3

\sqrt{\frac{GM}{4R^{3}}}


Option: 4

\sqrt{\frac{3\sqrt{3}GM}{8R^{3}}}


Answers (1)

best_answer

In \Delta AOB \Rightarrow \cos 60^{\circ}=\frac{R}{OB}\Rightarrow OB = 2R  (where OB is orbital radius)

Here gravitational force will provide the required centripetal force. 

Hence \frac{GMm}{(OB)^{2}}=m(OB)\omega ^{2}

\Rightarrow \omega= \sqrt{\frac{GM}{(OB)^{2}}}=\sqrt{\frac{GM}{(2R)^{3}}}\Rightarrow \omega = \sqrt{\frac{GM}{8R^{3}}}

Posted by

Nehul

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