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Q.
Two satellites A and B having masses in the ratio 4:3 are revolving in circular orbits of radii $3 r$ and $4 r$ respectively around the earth. The ratio of total mechanical energy of A to $B$ is :
Given that $\frac{ m _1}{ m _2}=\frac{4}{3}, \frac{ r _1}{ r _2}=\frac{3}{4}$
Now $TE =\frac{1}{2} mv ^2+\left(\frac{- GMm }{ r }\right)$
but $ \frac{ mv ^2}{ r }=\frac{ GMm }{ r ^2} \Rightarrow mv ^2=\frac{ GMm }{ r } $
$ \Rightarrow TE =-\frac{ GMm }{2 r } \propto \frac{ m }{ r } $
$ \frac{ TE _1}{ TE _2}=\frac{ m _1}{ m _2} \cdot \frac{ r _2}{ r _1}=\frac{4}{3} \times \frac{4}{3}=\frac{16}{9}$