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A rocket has to be launched from earth in such a way that it n

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A rocket has to be launched from earth in such a way that it never returns. If $E$ is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon.
(a) $\frac{E}{64}$
(b) $\frac{E}{16}$
(c) $\frac{E}{32}$
(d) $\frac{E}{4}$

Views: 5,852 students

Updated on: Oct 31, 2023

Book:

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

Exam:

JEE Mains 2019

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Camila Discussed

A rocket has to be launched from earth in such a way that it never returns. If

E

is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon.
(a)

\frac{E}{64}

(b)

\frac{E}{16}

(c)

\frac{E}{32}

(d)

\frac{E}{4}

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

E x p .

(b)
Given, volume of earth

(V_{e})

is 64 times of volume of moon

(V_{m})

, i.e.

\frac{V _{e}}{V _{m}} = 64 = \frac{\frac{4}{3} π R _{e}^{3}}{\frac{4}{3} π R _{m}^{3}}

where,

R_{e}

and

R_{m}

are the radius of earth and moon, respectively.
Then,

\frac{R _{e}}{R _{m}} = 4

Also, since the density of moon and earth are equal, i.e.

\Rightarrow \frac{M _{e}}{V _{e}} = \frac{M _{m}}{V _{m}}

, where

M_{e}

and

M_{m}

are the mass of br> the earth and moon, respectively.

\Rightarrow \frac{M _{e}}{M _{m}} = \frac{V _{e}}{V _{m}} = 64

The minimum energy or escape energy delivered by the rocket launcher, so that the rocket never returns to earth is

E_{e} = \frac{G M _{e} m}{R _{e}} = E

where,

m

is the mass of the rocket.
Similarly, minimum energy that a launcher should have to escape or to never return, if rocket is launched from surface of the moon is

E_{m} = \frac{G M _{m} m}{R _{m}}

∴

Ratio of escape energies

E_{e}

and

E_{m}

\frac{E _{e}}{E _{m}} = \frac{( \frac{G M _{e} m}{R _{e}} )}{( \frac{G M _{m} m}{R _{m}} )} = \frac{M _{e}}{M _{m}} \cdot \frac{R _{m}}{R _{e}}

= 64 \times \frac{1}{4} = 16

[using Eqs. (i) and (ii)]

∴ E_{m} = \frac{E _{e}}{16} = \frac{E}{16}

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Question Text	A rocket has to be launched from earth in such a way that it never returns. If $E$ is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon. (a) $\frac{E}{64}$ (b) $\frac{E}{16}$ (c) $\frac{E}{32}$ (d) $\frac{E}{4}$
Updated On	Oct 31, 2023
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 7
Upvotes	543
Avg. Video Duration	5 min

Text solutionVerified

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