A satellite moves around the earth in a circular orbit with speed `v`. If `m` is the mass of the satellite, its total energy is

Options

A. `(3)/(4)mv^(2)`
B. `(1)/(2)mv^(2)`
C. `mv^(2)`
D. `-((1)/(2))mv^(2)`

Answer

D

Explanation

When a satellite of mass m revolves closely around the earth, its total energy is given by
`E=-(GMm)/(2R)`
where M and R denote the mass and radius of the earth
`therefore E = -[(GM)/(R )][(m)/(2)]" "` ……(1)
But `v=sqrt((GM)/(R )) " " therefore v^(2)=(GM)/(R )" "` ....... (2)
`therefore` Using (2) in (1), we get
`E = v^(2)xx (m)/(2)=-(1)/(2)mv^(2)`