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Potential Energy of an Object at a Height

Two artificia...

Question

Two artificial satellites of masses $m_{1} a n d m_{2}$ are moving with speeds $v_{1} a n d v_{2}$ in orbits of radii $r_{1} a n d r_{2}$ respectively. If $r_{1} > r_{2}$ then which of the following statements is true.

A

v_{1} = v_{2}

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B

v_{1} > v_{2}

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C

v_{1} < v_{2}

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D

\frac{v_{1}}{r_{1}} \frac{v_{2}}{r_{2}}

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Solution

The correct option is C $v_{1} < v_{2}$
Orbital velocity, $v = \sqrt{\frac{G M}{r}}$ where r is the radius of orbit.
Thus for $r_{1} > r_{2} ⟹ v_{2} > v_{1}$

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