A solid sphere of uniform density and mass M has radius 4 m. Its centre is at the origin of the coordinate system. Two spheres of radii 1 m are taken out so that their centres are P (0, -2,0) and Q (0,2,0) respectively as shown in fig This leaves two spherical cavities.
What is the gravitational field at the origin of the coordinate axis ?

Question

A solid sphere of uniform density and mass M has radius 4 m. Its centre is at the origin of the coordinate system. Two spheres of radii 1 m are taken out so that their centres are P (0, -2,0) and Q (0,2,0) respectively as shown in fig This leaves two spherical cavities.

What is the gravitational field at the origin of the coordinate axis ?

Infinity Learn · Accepted Answer

Let p be the density of sphere, R radius of the sphere and r, radius of spherical cavitiesMass of complete sphere $$=43$$$$π$$$$R3$$ρ$$=MMass$$ of sphere removed $$=43$$$$π$$$$r3$$ρ$$=mHere$$ $$m=Mr3R3=M(1)3(4)3=M64Now$$ , $$IR=I+IP+IQ0=I+IP$$−IP ∵$$IQ=$$−IP  and  $$IP=0$$∴ $$I=0$$

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