Two identical satellites are at R and 7R away from earth surface,… - Vidyadip

MCQ

Two identical satellites are at $R$ and $7R$ away from earth surface, the wrong statement is ($R $ = Radius of earth)

A
Ratio of total energy will be $4$
B
Ratio of kinetic energies will be $4$
C
Ratio of potential energies will be $4$
✓
Ratio of total energy will be $4$ but ratio of potential and kinetic energies will be $2$

✓

Answer

Correct option: D.

Ratio of total energy will be $4$ but ratio of potential and kinetic energies will be $2$

d
(d)Orbital radius of satellites ${r_1} = R + R = 2R$
${r_2} = R + 7R = 8R$
${U_1} = \frac{{ - GMm}}{{{r_1}}}$ and ${U_2} = \frac{{ - GMm}}{{{r_2}}}$
${K_1} = \frac{{GMm}}{{2{r_1}}}$ and ${K_2} = \frac{{GMm}}{{2{r_2}}}$
${E_1} = \frac{{GMm}}{{2{r_1}}}$ and ${E_2} = \frac{{GMm}}{{2{r_2}}}$
$\frac{{{U_1}}}{{{U_2}}} = \frac{{{K_1}}}{{{K_2}}} = \frac{{{E_1}}}{{{E_2}}} = 4$

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