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(A) The potential energy $(PE)$ of a satellite at distance $r$ from the center of the Earth is given by $PE = -\frac{GMm}{r}$.For the two satellites,t

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Ratio of total energy of both is $5$

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(A) The potential energy $(PE)$ of a satellite at distance $r$ from the center of the Earth is given by $PE = -\frac{GMm}{r}$.For the two satellites,the distances from the center are $r_1 = R + R = 2R$ and $r_2 = R + 7R = 8R$.The ratio of potential energies is $\frac{PE_1}{PE_2} = \frac{r_2}{r_1} = \frac{8R}{2R} = 4$.Kinetic energy $(KE)$ is given by $KE = \frac{GMm}{2r}$,so the ratio $\frac{KE_1}{KE_2} = \frac{r_2}{r_1} = 4$.Total energy $(TE)$ is given by $TE = -\frac{GMm}{2r}$,so the ratio $\frac{TE_1}{TE_2} = \frac{r_2}{r_1} = 4$.Since the ratio of total energy is $4$,the statement in option $A$ (ratio is $5$) is incorrect. Also,the ratio of the magnitude of potential energy to kinetic energy is $|PE|/KE = |-\frac{GMm}{r}| / (\frac{GMm}{2r}) = 2$.

Two identical satellites are at heights $R$ and $7R$ from the Earth's surface. Which of the following statements is incorrect? ($R =$ radius of the Earth)

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