Search any question & find its solution
Question:
Answered & Verified by Expert
A launching vehicle carrying an artificial satellite of mass $m$ is set for launch on the surface of the earth of mass $M$ and radius $R$. If the satellite is intended to move in a circular orbit of radius $7 R$, the minimum energy required to be spent by the launching vehicle on the satellite is
$($ Gravitational constant $=G$ )
Options:
$($ Gravitational constant $=G$ )
Solution:
2647 Upvotes
Verified Answer
The correct answer is:
$-\frac{13 G M m}{14 R}$
The energy of artificial satellite at the surface of the earth
$E_1=-\frac{G M m}{R}$
When the satellite is intended to move in a circular orbit of radius $7 R$, then energy of artificial satellite
$E_2=-\frac{1}{2} \frac{G M m}{7 R}$
The minimum energy required
$E=E_1-E_2$
$=-\frac{G M m}{R}+\frac{1}{2}\left(\frac{G M m}{7 R}\right)$
$=\frac{-14 G M m+G M m}{14 R}$
$=-\frac{13 G M m}{14 R}$
$E_1=-\frac{G M m}{R}$
When the satellite is intended to move in a circular orbit of radius $7 R$, then energy of artificial satellite
$E_2=-\frac{1}{2} \frac{G M m}{7 R}$
The minimum energy required
$E=E_1-E_2$
$=-\frac{G M m}{R}+\frac{1}{2}\left(\frac{G M m}{7 R}\right)$
$=\frac{-14 G M m+G M m}{14 R}$
$=-\frac{13 G M m}{14 R}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.