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Physics · PYQ NEET UG 2024
हिन्दीThe minimum energy required to launch a satellite of mass \( m \) from the surface of earth of mass \( M \) and radius \( R \) in a circular orbit at an altitude of \( 2R \) from the surface of the earth is:
Correct answer · Option 3
\( \frac{5GmM}{6R} \)
Explanation
Initial energy at the surface of the Earth is \( E_i = -\frac{G M m}{R} \). The satellite orbits at radius \( r = R + 2R = 3R \), where total energy is \( E_f = -\frac{G M m}{2r} = -\frac{G M m}{6R} \). Thus, the required launch energy is \( \Delta E = E_f - E_i = -\frac{G M m}{6R} - (-\frac{G M m}{R}) = \frac{5 G M m}{6 R} \).
