Question

Two identical satellites are at the heights $R$ and $7R$ from the earth's surface. Then which of the following statement is incorrect: ($r=$ radius of the earth).

• A. ratio of total energy of both is $4$
• B. ratio of kinetic energy of both is $4$
• C. ratio of potential energy of both $4$
• D. ratio of total energy of both is $4$ and ratio of potential to kinetic energy is $2$

Answer 1

Answer: (D)

ratio of total energy of both is $4$ and ratio of potential to kinetic energy is $2$

$P.E=-\frac{GMm}{h}$ where $h$ is the distance of object from the center of earth.

For the two identical satellites, $h_1=2R;h_2=8R$

Thus $\frac{P.E_1}{P.E_2}=\frac{h_2}{h_1}=4$

Also, $K.E=-\frac{P.E}{2}⟹\frac{K.E_1}{K.E_2}=4$

Also, $T.E=\frac{P.E}{2}$ $⟹\frac{T.E_1}{T.E_2}=4$