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JIPMER 2012
Exam
JIPMER
Year
2012
Subject
Physics
Chapter
Gravitation

JIPMER 2012 · Physics · Gravitation

A launching vehicle carrying an artificial satellite of mass m is...

A launching vehicle carrying an artificial satellite of mass mm is set for launch on the surface of the earth of mass MM and radius RR. If the satellite is intended to move in a circular orbit of radius 7R7 R, the minimum energy required to be spent by the launching vehicle on the satellite is (Gravitational constant =G=G )

Options

  1. AGMmR\frac{G M m}{R}
  2. B−13GMm14R-\frac{13 G M m}{14 R}
  3. CGMm7R\frac{G M m}{7 R}
  4. D−GMm14R-\frac{G M m}{14 R}

Correct answer

B. −13GMm14R-\frac{13 G M m}{14 R}

Step-by-step solution

The energy of artificial satellite at the surface of the earth E1=−GMmRE_1=-\frac{G M m}{R} When the satellite is intended to move in a circular orbit of radius 7R7 R, then energy of artificial satellite E2=−12GMm7RE_2=-\frac{1}{2} \frac{G M m}{7 R} The minimum energy required E=E1−E2E=E_1-E_2 =−GMmR+12(GMm7R)=-\frac{G M m}{R}+\frac{1}{2}\left(\frac{G M m}{7 R}\right)=\frac{-14 G M m+G M m}{14 R} =-\frac{13 G M m}{14 R}
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