A satellite of mass , os revolving round the eartj at height of `10R`, where R is the radius of earth. What is the kinetic energy of satellite.

Options

A. `(mgR)/8`
B. `(mgR)/16`
C. `(mgR)/2`
D. `(mgR)/4`

Answer

A

Explanation

As we know that the kinetic energy of a revolving satellite at a height h above the earth's surface is given as
`KE=1/2mv^(2)=(GMm)/(2r)(becausev=(sqrt(GM))/r` for circular orbit `)`
`=(GMm)/(2(R+h))`
where, R is the radius of the earth.

Given , height of a satellite from the earth surface h = 3R and mass of the satellite = m
So, `KE=(GMm)/(2(R+3R))=(GMm)/(2(4R))`
`KE=(GMm)/(8R)xxR/R`
`thereforeGMmR/(8R^(2))=(gmR)/8`