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 P1 and P2 shown in the figure.

Here the point P1 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 P1 from the center of the sphere is x=4a -a +a = 4a

Therefore, electric field

Field at P2 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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