Q. 14

# A uniform metal sphere of radius α and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4α (figure 11-E2). The Centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P_{1} and P_{2} shown in the figure.

Answer :

Here the point P_{1} lies outside the sphere but inside the shell. We know the electric field inside the shell is zero. Therefore, only the sphere gives rise to the field.

The distance of P_{1} from the center of the sphere is x=4a -a +a = 4a

Therefore, electric field

Field at P_{2} is due to both the sphere and the shell.

The distance of from the center of the sphere is x = 4a+a+a = 6a.

Therefore, the field is

The distance of from the center of the sphere is x = 4a+a= 5a.

Therefore, the field is

The total electric field is thus

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