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# A man has constructed a toy as shown in fig. If the density of the material of the sphere is 12 times that of the cone then determine the position of the centre of mass. [Centre of mass of a cone of height h is at height of h4 from its base.]

Asked by rushabhjain.a 21st October 2019, 10:03 PM
Dimensions of the toy are shown in figure.

Centre of mass of solid cone is at 1/4 of height from base and is located at axis of cone as shown C in figure
Centre of mass of spolid sphere is at centre as shown C in figure.

mass of cone , mC = (1/3)π (2R)2 (4R) ρ = (16/3) πR3ρ = (16/3)α
where ρ is density of material of solid cone, and α = πR3ρ

mass of sphere, mS = (4/3)π (2R)3 12ρ= 128α

Centre of mass of toy = [ mC × R  + mS × 5R ] / ( mC + mS ) = [ (16/3)α R + ( 128α × 5R ) ] / ( (16/3)α + 128α ) = 4.84 R

Hence centre of mass of toy is at 4.84 R from base , located at axis of toy
Answered by Expert 22nd October 2019, 1:08 PM
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