A sphere of radius R has its centre at the origin. It has a uniform mass density ρ0 except that there is a spherical hole of radius r=R2 whose centre is at x=12R as shown in the figure. The magnitude of gravitational field at a point distance X on the x- axis (where X > R) is
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a
4GπR3ρ03[1X2−18(X−R2)2]
b
4GπR3ρ03[2X2−18(X−R2)2]
c
2GπR3ρ03[1X2−18(X−R2)2]
d
GπR3ρ03[1X2−18(X−R2)2]
answer is A.
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Detailed Solution
At point P, |Eg1−Eg2|=Eg m1=43πR3ρ0m2=43π(R2)3ρ0=43πR3ρ018Eg1=Gm1X2=G43πR3ρ0X2Eg2=Gm2(X−R2)2=G43πR3ρ018(X−R2)2∴ Eg=G43πR3ρ0[1X2−18(X−R2)2]