Question

A carpenter has constructed a toy as shown in figure. If the density of the material of the sphere is 12 tirnes that of cone, the `y-` coordinate of `COM` of toy point `O`

A. at a distance of `2 R` from `O`
B. at a distance of `3 R` from `O`
C. at a distance of `4 R` from `O`
D. at a distance of `5 R` from `O`

Answer 1

Correct Answer - C
( c) Let density of cone is `rho`, then density of sphere is `12 rho`.
Mass of cone :
`m_1 =(1)/(3) pi(2 R)^2(4 R) rho = 16 pi R^3//3`
mass of sphere : `m_2 = (4)/(3) pi R^3(12 rho) = 48 pi rho R^3//3`
`y_(cm) = (m_1 OQ_1 + m_2 OQ_2)/(m_1 + m_2)`
=`((16 pi rho R^3)/(3)((4 R)/(4))+(48)/(3)pi rho R^3(5 R))/((16 pi rho R^3)/(3) + (48 pi rho R^3)/(3)) = 4 R`.