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A satellite of mass m is in a circular o...

A satellite of mass `m` is in a circular orbit of radius `2R_(E)` about the earth. The energy required to transfer it to a circular orbit of radius `4R_(E)` is (where `M_(E)` and `R_(E)` is the mass and radius of the earth respectively)

A

`(GM_(E)m)/(2R_(E))`

B

`(GM_(E)m)/(4R_(E))`

C

`(GM_(E)m)/(8R_(E))`

D

`(GM_(E)m)/(16R_(E))`

Text Solution

Verified by Experts

The correct Answer is:
C
( c) Initial total energy of the satellite is
`E_(i)=-(GM_(E)m)/(4R_(E))`
Final total energy of the satellite is
`E_(f)=-(GM_(E)m)/(8R_(E))`
The change in the total energy is
`DeltaE=E_(f)-E_(i)`
`DeltaE=-(GM_(E)m)/(8R_(E))-(-(GM_(E)m)/(4R_(E)))`
`=-(GM_(E)m)/(8R_(E))+(GM_(E)m)/(4R_(E))=(GM_(E)m)/(8R_(E))`
Thus, the energy required to transfer the satellite to the desired orbit `=(GM_(E)m)/(8R_(E))`
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