A spherical cavity of radius R/2 is made in a sphere of radius R and mass M. The centre of the cavity is at a distance R/2 from the centre of the sphere. The intensity of gravitational field at the centre of cavity is :-
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Question

A spherical cavity of radius R/2 is made in a sphere of radius R and mass M. The centre of the cavity is at a distance R/2 from the centre of the sphere. The intensity of gravitational field at the centre of cavity is :-

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G1 Physics · Accepted Answer

Rₑpresent the cavity by superposing a sphere of density -ρ inside the original sphere. The field inside the cavity is uniform and equals (4πGρ/3)d, where d = R/2 is the separation of centres. For the original sphere, ρ = 3M/(4πR³). Hence g = (4πG/3)(3M/4πR³)(R/2) = GM/(2R²). Correct answer: C.