SATHEE: Gravitation 3 Question 3

Gravitation 3 Question 3

6. What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ ?

(2013 Main)

(a) $\frac{5 G m M}{6 R}$

(b) $\frac{2 G m M}{3 R}$

(d) $\frac{G m M}{3 R}$

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Answer:

Correct Answer: 6. (c)

Solution:

$E$ = Energy of satellite - energy of mass on the surface of planet

$= - \frac{G M m}{2 r} - \frac{G M m}{R}$

Here, $r = R + 2 R = 3 R$

Substituting in about equation we get, $E = \frac{5 G M m}{6 R}$

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Gravitation 3 Question 3

6. What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R ?

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6. What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ ?