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NEET 2024
Exam
NEET
Year
2024
Subject
Physics
Chapter
Gravitation

NEET 2024 · Physics · Gravitation

The minimum energy required to launch a satellite of mass m from...

The minimum energy required to launch a satellite of mass mm from the surface of earth of mass MM and radius RR in a circular orbit at an altitude of 2R2 R from the surface of the earth is:

Options

  1. A2GmM3R\frac{2 G m M}{3 R}
  2. BGmM2R\frac{G m M}{2 R}
  3. CGmM3R\frac{G m M}{3 R}
  4. D5GmM6R\frac{5 G m M}{6 R}

Correct answer

D. 5GmM6R\frac{5 G m M}{6 R}

Step-by-step solution

Apply energy conservation, Ui+Ki=Uf+Kf⇒−GMmR+Ki=−GMm3R+12mv2⇒−GMmR+Ki=−GMm3R+12×m×GM3R⇒Ki=−16GMmR+GMmRKi=56GMmR\begin{gathered} 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{gathered}
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