For a satellite moving in an orbit around the earth, ratio of kinetic energy to potential energy is

Options

A. 1
B. `sqrt2`
C. `(1)/(2)`
D. `(1)/(sqrt2)`

Answer

C

Explanation

For a satellite, moving in a circular orbit of radius r, orbital velocity `v_(0)=sqrt((GM)/(r ))`
`therefore` Its `K.E. =(1)/(2)mv_(0)^(2)=(1)/(2)m(GM)/(r )=(1)/(2)(GMm)/(r )`
and its `P.E.=(GMm)/(r )` (in magnitude)
`therefore (K.E.)/(P.E.)=(GMm)/(2r)xx(r )/(GMm)=(1)/(2)`
Note : We can directly use `P.E.=-2 (K.E.)` for a satellite.
`therefore (K.E.)/(P.E.)=(1)/(2)` (in magnitude)