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A solid sphere of mass M and radius a is surrounded by a unifo

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A solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2 a$ and $2 M$ . The gravitational field at distance $3 a$ from the centre will be
(a) $\frac{GM}{9 a ^{2}}$

(b) $\frac{2 GM}{9 a ^{2}}$

(c) $\frac{GM}{3 a ^{2}}$

(d) $\frac{2 GM}{3 a ^{2}}$

Name: Video solution 1: A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and 2M. The gravitational field at distance 3a from the centre will be(a) 9a2GM(b) 9a22GM(c) 3a2GM(d) 3a22GM
Uploaded: 2022-12-02T17:55:23.000Z
Duration: 12 min
Description: Video solution 1: A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and 2M. The gravitational field at distance 3a from the centre will be(a) 9a2GM(b) 9a22GM(c) 3a2GM(d) 3a22GM

Views: 5,429 students

Updated on: Dec 2, 2022

Book:

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

Exam:

JEE Mains 2019

Found 8 tutors discussing this question

Noah Discussed

A solid sphere of mass

M

and radius

a

is surrounded by a uniform concentric spherical shell of thickness

2 a

and

2 M

. The gravitational field at distance

3 a

from the centre will be
(a)

\frac{GM}{9 a ^{2}}

(b)

\frac{2 GM}{9 a ^{2}}

(c)

\frac{GM}{3 a ^{2}}

(d)

\frac{2 GM}{3 a ^{2}}

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Exp. (c)
According to question, diagram will be as follows
Solution Image

Gravitational field due to solid sphere of radius a at a distance,

r = 3 a

, i.e.

(r > R)

E_{1} = \frac{GM}{r ^{2}} = \frac{GM}{( 3 a ) ^{2}} = \frac{GM}{9 a ^{2}}

Similarly, gravitational field due to spherical shell at a distance,

r = 3 a

,
i.e.

E_{2} = \frac{GM}{R ^{2}} = \frac{G ( 2 M )}{( 3 a ) ^{2}} = \frac{2 GM}{9 a ^{2}}

Both fields are attractive in nature, so direction will be same.
Net field,

E_{n e t} = \frac{GM}{9 a ^{2}} + \frac{2 GM}{9 a ^{2}}

E_{n e t} = \frac{GM}{3 a ^{2}}

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Question Text	A solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2 a$ and $2 M$ . The gravitational field at distance $3 a$ from the centre will be (a) $\frac{GM}{9 a ^{2}}$ (b) $\frac{2 GM}{9 a ^{2}}$ (c) $\frac{GM}{3 a ^{2}}$ (d) $\frac{2 GM}{3 a ^{2}}$
Updated On	Dec 2, 2022
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	130
Avg. Video Duration	12 min

Text solutionVerified

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A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and 2M. The gravitational field at distance 3a from the centre will be(a) 9a2GM​(b) 9a22GM​(c) 3a2GM​(d) 3a22GM​

Text solutionVerified

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

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