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.

Now \(T E=\frac{1}{2} mv ^{2}+\left(\frac{- GMm }{ r }\right)\)

but \(\frac{ mv ^{2}}{ r }=\frac{ GMm }{ r ^{2}} \Rightarrow mv ^{2}=\frac{ GMm }{ r }\)

\(\Rightarrow TE =-\frac{ GMm }{2 r } \propto \frac{ m }{ r }\)

\(\frac{T E_{1}}{T_{2}}=\frac{m_{1}}{m_{2}} \cdot \frac{r_{2}}{r_{1}}=\frac{4}{3} \times \frac{4}{3}=\frac{16}{9}\)