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  4. The ratio of binding energy of a satellite at rest on earth’s surface to the binding energy of a satellite of same mass revolving around the earth at a height h above the earth’s surface is (R = radius of the earth)

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Q. The ratio of binding energy of a satellite at rest on earth’s surface to the binding energy of a satellite of same mass revolving around the earth at a height $h$ above the earth’s surface is (R = radius of the earth)

MHT CETMHT CET 2017Gravitation

Solution:

Binding energy of satellite
$E _{ s }=\frac{ GMm }{2( R + h )}$
Binding energy of body at rest
$E _{ r }=\frac{ GMm }{ R }$
$\frac{ E _{ r }}{ E _{ s }}=\frac{2( R + r )}{ R }$