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Standard XII

Physics

Satellites

Two satellite...

Question

Two satellite A and B of same mass orbit the Earth in orbit of radius R and 3R respectively. Compare the centripetal force $F_{A}$ on satellite A and $F_{B}$ on satellite B.

F_{A} = 9 F_{B}

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F_{A} = 3 F_{B}

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F_{A} = F_{B}

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F_{B} = 3 F_{A}

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F_{B} = 9 F_{A}

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Solution

The correct option is A $F_{A} = 9 F_{B}$
Given : $r_{A} = R$ $r_{B} = 3 R$ $M_{A} = M_{B} = M$
Let the mass of earth be $M^{'}$ .
Centripetal force on the satellite A $F_{A} = \frac{G M^{'} M_{A}}{r_{A}^{2}} = \frac{G M^{'} M}{R^{2}}$

Similarly centripetal force on the satellite B $F_{B} = \frac{G M^{'} M_{B}}{r_{B}^{2}} = \frac{G M^{'} M}{(3 R)^{2}} = \frac{G M^{'} M}{9 R^{2}}$

$⟹$ $F_{A} = 9 F_{B}$

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Two satellite A and B of same mass orbit the Earth in orbit of radius R and 3R respectively. Compare the centripetal force FAon satellite A and FB on satellite B.

The correct option is A FA=9FBGiven : rA=R rB=3R MA=MB=MLet the mass of earth be M′.Centripetal force on the satellite A FA=GM′MAr2A=GM′MR2Similarly centripetal force on the satellite B FB=GM′MBr2B=GM′M(3R)2=GM′M9R2⟹ FA=9FB

Two satellite A and B of same mass orbit the Earth in orbit of radius R and 3R respectively. Compare the centripetal force $F_{A}$ on satellite A and $F_{B}$ on satellite B.