Assertion : Let `W_(1)` be the work done in taking away a satellite from the surface of earth to its orbit and then `W_(2)` the work done in rotating the satellite in circular orbit there. Then, `W_(1)=W_(2)`
Reason : `W_(2)=(GMm)/(4R)`

Options

A. If both Assertin and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is false
D. If Assertion is false but Reason is true

Answer

D

Explanation

`W_(1)=(1)/(2)mv^(2)=(1)/(2)m(sqrt((GM)/(r)))^(2)=(GMm)/(2r)=(GMm)/(4R)`
`W_(1)=DeltaU=(mgh)/(1+(h)/(R))=(mgRh)/(R+h)`
`=(m((GM)/(R^(2)))Rh)/(r)=((GMm)/(rR))h=(GMm)/(r)`.