A satellite of mass m is revolving round the earth at a height R above surface of earth. If g is gravitational intensity at earth's surface and R is radius of the earth, the K.E. of satellite is :

Options

A. `"mg" (R )/(4)`
B. `"mg"(R )/(2)`
C. `"mg" R`
D. `"2mg" R`

Answer

A

Explanation

Here gravitational force provides centripetal force
`therefore (mv^(2))/(2R)=(GMm)/((2R)^(2)) rArr (1)/(2)mv^(2)=(GMm)/(4R)=(mgR)/(4)`
or `K.E.=-(1)/(2) (GP.E.)= -(1)/(2)`
`((-GMm)/(2R))=(GMm)/(4R)=(mgR)/(4)`
Thus correct choice is (a).