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MHT CET 2024 (2 May, Shift 2) · Satellite Energy & Weightlessness

Satellite Energy & Weightlessness question from MHT CET 2024 (2 May, Shift 2)

Q10MHT CET 2024 · 2 MAY · SHIFT 2Medium

Satellite Energy & Weightlessness

The gravitational potential energy required to raise a satellite of mass ' $m$ ' to height ' $h$ ' above the earth's surface is ' $E_1$ '. Let the energy required to put this satellite into the orbit at the same height be ' $E_2$ '. If $M$ and $R$ are the mass and radius of the earth respectively then $E_1 : E_2$ is

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Answer: (d)

$E_1 = \Delta U = GMm\left(\frac{1}{R} - \frac{1}{R+h}\right) = \frac{GMmh}{R(R+h)}$ .
$E_2$ = orbital kinetic energy given at that height $= \frac{GMm}{2(R+h)}$ .
$\frac{E_1}{E_2} = \frac{2h}{R}$ .
So the answer is (d) $2h : R$ .

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