A cavity of radius $$R/2$$ is made inside a solid sphere of radius R. The centre of the cavity is located at a distance $$R/2$$ from the centre of the sphere. The gravitational force on a particle of mass ‘m’ at a distance $$R/2$$ from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite$$ to the centre of $$cavity) [Here $$g=GM/R2$$ , where M is the mass of the sphere]

Question

A cavity of radius $$R/2$$ is made inside a solid sphere of radius R. The centre of the cavity is located at a distance $$R/2$$ from the centre of the sphere. The gravitational force on a particle of mass ‘m’ at a distance $$R/2$$ from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite$$ to the centre of $$cavity) [Here $$g=GM/R2$$ , where M is the mass of the sphere]

Infinity Learn · Accepted Answer

$$gnet=g1$$−$$g2=GmR2R3$$−$$Gm8R2=Gm2R2$$−$$Gm8R2=Gm2R21$$−$$14=Gm2R234=3Gm8R2F=mg=3GMm8R2=3mg8$$

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