Q.

A carpenter has constructed a toy as shown in the figure. If the density of the material of the sphere is 12 times that of cone, the position of the centre of mass of the toy is given by:

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a

at a distance of 2R from O

b

at a distance of 3R from O

c

at a distance of 4R from O

d

at a distance of 5R from O

answer is C.

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Detailed Solution

Let density of cone is ρ, then density of sphere is 12ρ.Mass of cone:m1 = 13π(2R)2(4R)ρ = 16πρR33mass of sphere: m2 = 43πR3(12ρ) = 48πρR33ycm = m1OQ1+m2OQ2m1+m2       = 16πρR33(4R4)+483πρR3(5R)16πρR33+48πρR33 = 4R
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A carpenter has constructed a toy as shown in the figure. If the density of the material of the sphere is 12 times that of cone, the position of the centre of mass of the toy is given by: