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A synchronous satellite goes around the ...

A synchronous satellite goes around the earth one in every 24 h. What is the radius of orbit of the synchronous satellite in terms of the earth's radius ? (Given: Mass of the earth , `M_(E)=5.98xx10^(24) kg,` radius of the earth, `R_(E)=6.37xx10^(6)m`, universal constant of gravitational , `G=6.67xx10^(-11)Nm^(2)kg^(-2)`)

A

`2.4R_(E)`

B

`3.6R_(E)`

C

`4.8R_(E)`

D

`6.6R_(E)`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) The time period of satellite is
`T=2pisqrt((r_(3))/(GM_(E)))`
Squaring both sides, we get
`T^(2)=(4pi^(2)r^(3))/(GM_(E))`
`r^(3)=(T^(2)GM_(E))/(4pi^(2)) implies r= ((T^(2)GM_(E))/(4pi^(2)))^(1//3)`
Here, `T=24h=24xx60xx60 s`
`G=6.67xx10^(-11) N m^(2) kg^(-2)`
`M_(E)=5.98xx10^(24)kg`
`r=(((24xx60xx60)^(2)xx6.67xx10^(-11)xx5.98xx10^(24))/(4xx(3.14)^(2)))^(1//3)`
`=42.1xx10^(6) m`
`:. ( r)/(R_(E))=(42.1xx10^(6))/(6.37xx10^(6))=6.6 implies r=6.6R_(E)`
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