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- GM(R+a)2⎛⎜ ⎜ ⎜ ⎜ ⎜⎝1−18(1−R2a)2⎞⎟ ⎟ ⎟ ⎟ ⎟⎠
- GMa2⎛⎜ ⎜ ⎜ ⎜ ⎜⎝1−18(1−R2a)2⎞⎟ ⎟ ⎟ ⎟ ⎟⎠
- GM(R−a)2⎛⎜ ⎜ ⎜ ⎜ ⎜⎝1−18(1−2aR)2⎞⎟ ⎟ ⎟ ⎟ ⎟⎠
- GMR2⎛⎜ ⎜⎝1−18(1−2Ra)2⎞⎟ ⎟⎠

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Solution

Verified by Toppr

mass of metal sphere M=ρ.43πR3

mass of hollow sphere , m=ρ.43π(R/2)3=M/8

The field at that point = field due to metal sphere − field due to hollow sphere.

f=GMa2−Gm(a−R2)2=GMa2−GM8(a−R2)2=GMa2−GM8a2(1−R2a)2=GMa2⎛⎝1−18(a−R2a)2⎞⎠

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