A non – homogeneous sphere of radius R has the following density variation ρ$$=$$ρ$$0$$ for r≤$$R/3$$ ρ$$=$$ρ$$02$$ for $$R3$$

Question

A  non – homogeneous sphere of radius R has the following density variation  ρ$$=$$ρ$$0$$  for  r≤$$R/3$$     ρ$$=$$ρ$$02$$  for $$R3$$< r≤$$3R4and$$     ρ$$=$$ρ$$08$$  for $$3R4$$

Infinity Learn · Accepted Answer

For  $$r=5R6$$,up $$toR3$$,ρ$$=$$ρ$$0$$,     between $$R3and3R4$$,       ρ$$=$$ρ$$02$$     and  between $$3R4$$     and $$5R6$$,     ρ$$=$$ρ$$08$$     ∴      The mass of the sphere of radius $$5R/6$$ $$ism=43$$π$$(R3)3$$ρ$$0+$$[$$43$$π$$(3R4)3$$−$$43$$π$$(R3)3$$]ρ$$0/2$$     $$+$$[$$43$$π$$(5R6)3$$−$$43$$π$$(3R4)3$$]ρ$$0/8$$     $$=0.332$$ π$$R3$$ρ$$0$$     ∴      Gravitational field at a distance, $$r=5R6$$     $$isEg=Gm(5R/6)2$$     $$=G$$×$$0.332$$$$π$$$$R3$$ρ$$025R2$$×$$36$$     $$=0.48$$$$π$$GRρ$$0$$

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A non – homogeneous sphere of radius R has the following density variation ρ=ρ0 for r≤R/3 ρ=ρ02 for R3< r≤3R4and ρ=ρ08 for 3R4 <r≤R The gravitational field due to the sphere at r=5R6 is

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