A satellite of mass m is revolving around the earth at a distancer r from the centre of the earth. What is its total energ?

Options

A. `-(GMm)/( r)`
B. `-(GMm)/(2r)`
C. `-(2GMm)/( r)`
D. `+(GMm)/(2r)`

Answer

B

Explanation

The revolving satellite has two energies
(1) Gravitational P.E. `(U)=-(GMm)/(r )" "` …..(1)
and (2) `K.E.(K)=(1)/(2)mv_(e)^(2)=(1)/(2)m((GM)/(r ))`
`=(GMm)/(2r) " "` …….(2)
where `v_(c )`= orbital velocity `= (GM)/(r )`
`therefore` Total energy `= U+K=-(GMm)/(r )+(GMm)/(2r)`
`therefore E = -(GMm)/(2r)`