NEETPhysicsGravitationMCQ+4 / −1
The minimum energy required to launch a satellite of mass from the surface of earth of mass and radius in a circular orbit at an altitude of from the surface of the earth is:
- A
- B
- C
- D
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Correct answer: A
Apply energy conservation,
$$\begin{aligned} & U_i+K_i=U_f+K_f \\ & \Rightarrow \quad-\frac{G M m}{R}+K_i=-\frac{G M m}{3 R}+\frac{1}{2} m v^2 \\ & \Rightarrow \quad-\frac{G M m}{R}+K_i=-\frac{G M m}{3 R}+\frac{1}{2} \times m \times \frac{G M}{3 R} \\ & \Rightarrow \quad K_i=-\frac{1}{6} \frac{G M m}{R}+\frac{G M m}{R} \\ & K_i=\frac{5}{6} \frac{G M m}{R} \end{aligned}$$
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