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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 | 21 Oct, 2019, 22:03: PM
answered-by-expert Expert Answer
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 Thiyagarajan K | 22 Oct, 2019, 13:08: PM

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