Question

The ratio of energy required to raise a satellite to a height `(2R)/3` above earth's surface to that required to put it into the orbit at the same height is ______.

R = radius of the earth

पर्याय

• 2 : 1

• 3 : 2

• 3 : 1

• 4 : 3

Answer 1

The ratio of energy required to raise a satellite to a height `(2R)/3` above earth's surface to that required to put it into the orbit at the same height is 4 : 3.

Explanation:

Energy required to raise the satellite to a height h from surface of earth is given by

`"U"=-(GMm)/(R+h)-(-(GMm)/R)`

`=(GMm)/R-(GMm)/(R+h)=GMm[1/R-1/(R+h)]`

`=GMm[(R+h-R)/(R(R+h))]=GMm h/(R(R+h))`

KE of the satellite is given by

`K=1/2mV_0^2=1/2m(GM)/(R+h)`

`therefore U/K=(GMmh)/(R(R+h))xx((R+h)2)/(mGM)=(2h)/R`

`=2/Rxx(2R)/3=4/3`