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What is the minimum energy required to launch a satellite of m

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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 $2 R$ ?
(a) $\frac{5 G m M}{6 R}$
(b) $\frac{2 G m M}{3 R}$
(c) $\frac{G m M}{2 R}$
(d) $\frac{G m M}{3 R}$

Views: 7,145 students

Updated on: May 9, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2013

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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

?
(a)

\frac{5 G m M}{6 R}

(b)

\frac{2 G m M}{3 R}

(c)

\frac{G m M}{2 R}

(d)

\frac{G m M}{3 R}

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Exp. (a)
From conservation of energy,
Total energy at the planet
= Total energy at altitude

- \frac{GM m}{R} + (K E)_{s u r f a ce} = - \frac{GM m}{3 R} + \frac{1}{2} m v_{A}^{2} \dots (i)

In the orbital of planet, the necessary centripetal force is obtained by gravitational force.

∴ \frac{m v _{A}^{2}}{R + 2 R} = \frac{GM m}{( R + 2 R ) ^{2}}

\Rightarrow \frac{v _{A}}{2} = \frac{GM}{3 R}

From Eqs. (i) and (ii), we get

(KE)_{s u r f a ce} = \frac{5}{6} \frac{GMm}{R}

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Question Text	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 $2 R$ ? (a) $\frac{5 G m M}{6 R}$ (b) $\frac{2 G m M}{3 R}$ (c) $\frac{G m M}{2 R}$ (d) $\frac{G m M}{3 R}$
Updated On	May 9, 2023
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 8
Upvotes	1012
Avg. Video Duration	7 min

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 $2 R$ ?
(a) $\frac{5 G m M}{6 R}$
(b) $\frac{2 G m M}{3 R}$
(c) $\frac{G m M}{2 R}$
(d) $\frac{G m M}{3 R}$

Text solutionVerified

Filo tutor solutions (8)

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Text solutionVerified

Filo tutor solutions (8)

Questions from JEE Mains 2013 - PYQs

Practice questions from Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

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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 $2 R$ ?
(a) $\frac{5 G m M}{6 R}$
(b) $\frac{2 G m M}{3 R}$
(c) $\frac{G m M}{2 R}$
(d) $\frac{G m M}{3 R}$