Gravitation Question 347
Question: A satellite is launched in the equatorial plane in such a way that it can transmit signals up to $ [60{}^\circ ] $ latitude on the earth. The angular velocity of the satellite is
Options:
A) $ [\sqrt{\frac{GM}{8R^{3}}}] $
B) $ [\sqrt{\frac{GM}{2R^{3}}}] $
C) $ [\sqrt{\frac{GM}{4R^{3}}}] $
D) $ [\sqrt{\frac{3\sqrt{3}GM}{8R^{3}}}] $
Show Answer
Answer:
Correct Answer: A
Solution:
-
In $ [\Delta AOB: cos 60{}^\circ= R\RightarrowOB = 2R] $
Here gravitational force will provide the required centripetal force.
Hence.$ [\frac{GMm}{{{\left( OB \right)}^{2}}}=m\left( OB \right){{\omega }^{2}}] $ $ [\Rightarrow \omega =\sqrt{\frac{GM}{{{(OB)}^{3}}}}=\sqrt{\frac{GM}{{{(2R)}^{3}}}}\Rightarrow \omega =\sqrt{\frac{GM}{8R^{3}}}] $
