Question

Two satellites of earth, $ S_1 $ and $ S_2 $ , are moving in the same orbit. The mass of $ S_1 $ is four times the mass of $ S_2 $ . Which one of the following statements is true ?

• A. The time period of $ S_1 $ is four times that of $ S_2 $
• B. The potential energies of earth and satellite in the two cases are equal
• C. $ S_1 $ and $ S_2 $ are moving with the same speed
• D. The kinetic energies of the two satellites are equal

Answer 1

The Correct Option is C

\(K.E. =\frac{ GMm }{2r}\) \(\Rightarrow\) Kinetic energies are unequal.
\(T =\frac{2 \pi r ^{\frac 32}}{\sqrt{ GM }}\) \(\Rightarrow\) Time period are equal.
P.E. \(=-\frac{\text {GMm}}{r}\) \(\Rightarrow\) Potential energies are unequal.
\(v =\sqrt{\frac{ GM }{ r }}\) \(\Rightarrow\) Orbital speeds are equal.

So, the cortrect option is (C): \(S_1\)​ and \(S_2\)​ are moving with the same speed.