Question 229: Gravitation

Question

Energy required to move a body of mass $m$ from an orbit of radius $2R$ to $3R$ is

Accepted Answer

Gravitational potential energy E = $ - {{GMm} \over r}$
where  M = mass of earth
m = mass of body
r = radius of earth
Energy required to move a body of mass $m$ from an orbit of radius $2R$ to $3R$
$=$ (Potential energy of the Earth-mass system when mass is at distance $3R$ ) $-$ (Potential energy of the Earth-mass system when mass is at distance $2R$)
$ = {{ - GMm} \over {3R}} - \left( {{{ - GMm} \over {2R}}} \right)$
$ = {{ - GMm} \over {3R}} + {{GMm} \over {2R}}$
$ = {{ - 2GMm + 3GMm} \over {6R}} = {{GMm} \over {6R}}$

Answer

${{GMm} \over {12{R^2}}}$

Answer

${{GMm} \over {3{R^2}}}$

Answer

${{GMm} \over {8R}}$

Answer

${{GMm} \over {6R}}$

Gravitation

Energy required to move a body of mass m from an orbit of radius 2R to 3R is

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