The magnitudes of gravitational field at distances r₁ and r₂ from the centre of a uniform sphere of radius R and mass M are F₁ and F₂, respectively. Then

detailed solution

Correct option is C

We consider the following two cases(i) When r1 > R and r2 > R i.e., the points are outside the sphere. In this case, the gravitational field is given by GM /r2.SoF1=GMr12  and  F2=GMI22or F1F2=r22r12 i.e., option (b) is correct(ii) When r1 <.R i.e .,the points are inside the sphere. In this caseGravitational field =GM1r2where M1, is the mass of the body within the sphere of radius r.∴ M1=43πr3ρ where p is the densityF1=G43πr13ρ/r12and F2=G43πr23ρ/r22or F1F2=r1r2 4,i.e option (a) is correct.