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)

Question

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) (A) (2(R + h)/R) (B) (R + h/2R) (C) (R + h/R) (D) (R/R + h)

Tardigrade Admin · Accepted Answer

Binding energy of satellite E s =( GMm /2( R + h )) Binding energy of body at rest E r =( GMm / R ) ( E r / E s )=(2( R + r )/ R )

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)

$\frac{2 ( R + h )}{R}$

$\frac{R + h}{2 R}$

$\frac{R + h}{R}$

$\frac{R}{R + h}$

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

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)

R2(R+h)​

2RR+h​

RR+h​

R+hR​