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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