A communication satellite of earth which takes $24 h r$ . to complete one circular orbit eventually has to be replaced by another satellite of double mass. If the new satellites also has an orbital time period of $24 h r s$ , then what is the ratio of the radius of the new orbit to the original orbit ?

1 : 1

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2 : 1

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\sqrt{2} : 1

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1 : 2

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Solution

The correct option is B $1 : 1$
Time period of revolution of satellite, $T = \sqrt{\frac{r^{3}}{G M_{e}}}$ where $r$ and $M_{e}$ are the radius of the orbit and mass of earth.

Thus time period doesn't depend on the mass of satellite.

$⟹$ for same time period, radius of the orbit will be same.
Hence $r^{'} : r = 1 : 1$

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A communication satellite of earth which takes 24hr. to complete one circular orbit eventually has to be replaced by another satellite of double mass. If the new satellites also has an orbital time period of 24hrs, then what is the ratio of the radius of the new orbit to the original orbit ?

The correct option is B 1:1Time period of revolution of satellite, T=√r3GMe where r and Me are the radius of the orbit and mass of earth.Thus time period doesn't depend on the mass of satellite.⟹ for same time period, radius of the orbit will be same.Hence r′:r=1:1