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A uniform metal sphere of radius R and mass m is surrounded by

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Solving time: 4 mins

A uniform metal sphere of radius $R$ and mass $m$ is surrounded by a thin uniform spherical shell of same mass and radius $4 R$ . The centre of the shell $C$ falls on the surface of the inner sphere. Find the gravitational fields at points $A$ and $B$ .

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Book:

Mechanics Volume 2 (DC Pandey)

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Eleanor Discussed

A uniform metal sphere of radius

R

and mass

m

is surrounded by a thin uniform spherical shell of same mass and radius

4 R

. The centre of the shell

C

falls on the surface of the inner sphere. Find the gravitational fields at points

A

and

B

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

(i) At point

A

, field strength due to shell will be zero. Net field is only due to metal sphere. Distance between centre of metal sphere and point

A

4 R

∴ E_{A} = \frac{G ( m )}{( 4 R ) ^{2}} = \frac{G m}{16 R ^{2}}

(ii) At point

B

, net field is due to both, due to shell and due to metal sphere.

∴ E_{B} = \frac{G m}{( 5 R ) ^{2}} + \frac{G m}{( 6 R ) ^{2}} = \frac{61 G m}{900 R ^{2}}

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Question Text	A uniform metal sphere of radius $R$ and mass $m$ is surrounded by a thin uniform spherical shell of same mass and radius $4 R$ . The centre of the shell $C$ falls on the surface of the inner sphere. Find the gravitational fields at points $A$ and $B$ .
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	139

A uniform metal sphere of radius $R$ and mass $m$ is surrounded by a thin uniform spherical shell of same mass and radius $4 R$ . The centre of the shell $C$ falls on the surface of the inner sphere. Find the gravitational fields at points $A$ and $B$ .

Text solutionVerified

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A uniform metal sphere of radius R and mass m is surrounded by a thin uniform spherical shell of same mass and radius 4R. The centre of the shell C falls on the surface of the inner sphere. Find the gravitational fields at points A and B.

Text solutionVerified

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A uniform metal sphere of radius $R$ and mass $m$ is surrounded by a thin uniform spherical shell of same mass and radius $4 R$ . The centre of the shell $C$ falls on the surface of the inner sphere. Find the gravitational fields at points $A$ and $B$ .