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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Solution

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

(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 is 4R. ∴ EA=G(m)(4R)2=Gm16R2(ii) At point B, net field is due to both, due to shell and due to metal sphere. ∴ EB=Gm(5R)2+Gm(6R)2=61Gm900R2

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.