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Question

(B) The total mechanical energy $E$ of a satellite of mass $m$ orbiting at a distance $r$ from the center of the Earth is given by $E = -\frac{GMm}{2r

Vedclass · Accepted Answer

$16: 9$

Vedclass · Answer

(B) The total mechanical energy $E$ of a satellite of mass $m$ orbiting at a distance $r$ from the center of the Earth is given by $E = -\frac{GMm}{2r}$.From this expression,we can see that $E \propto \frac{m}{r}$.Given the mass ratio $\frac{m_A}{m_B} = \frac{4}{3}$ and the radius ratio $\frac{r_A}{r_B} = \frac{3r}{4r} = \frac{3}{4}$.Therefore,the ratio of the total mechanical energy of $A$ to $B$ is $\frac{E_A}{E_B} = \frac{m_A}{m_B} 	imes \frac{r_B}{r_A}$.Substituting the given values: $\frac{E_A}{E_B} = \frac{4}{3} 	imes \frac{4}{3} = \frac{16}{9}$.

Two satellites $A$ and $B$ having masses in the ratio $4: 3$ are revolving in circular orbits of radii $3r$ and $4r$ respectively around the earth. The ratio of total mechanical energy of $A$ to $B$ is.

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