Two identical satellites are at 7 R and R away from earth surface- the wrong statement is R - Radius of earthA- Ratio of total energy will be 4B- Ratio of potential energies will be 4C- Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2D- Ratio of kinetic energies will be 4

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Question

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

Ratio of total energy will be 4

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Ratio of kinetic energies will be 4

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Ratio of potential energies will be 4

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

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Solution

The correct option is D Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2
$O r b i t a l r a d i u s o f s a t e l l i t e s r_{1} = R + R = 2 R r_{2} = R + 7 R = 8 R U_{1} = \frac{- G M m}{r_{1}} a n d U_{2} = \frac{- G M m}{r_{2}} K_{1} = \frac{G M m}{2 r_{1}} a n d K_{2} = \frac{G M m}{2 r_{2}} E_{1} = \frac{- G M m}{2 r_{1}} a n d E_{2} = \frac{- G M m}{2 r_{2}} ∴ \frac{U_{1}}{U_{2}} = \frac{K_{1}}{K_{2}} = \frac{E_{1}}{E_{2}} = 4$

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

The correct option is D Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2Orbital radius of satellites r1=R+R=2Rr2=R+7R=8RU1=−GMmr1 and U2=−GMmr2K1=GMm2r1 and K2=GMm2r2E1=−GMm2r1 and E2=−GMm2r2∴U1U2=K1K2=E1E2=4