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`

Options

A. `3R`
B. `(9R)/(2)`
C. `(7R)/(2)`
D. `4R`

Answer

D

Explanation

Mass of cone `M_(1)=rho((1)/(3) pi (2R^(2))4R)`
`c=(rho)/(3)pi (16R^(3))`
mass of sphere `M_(2)`
`=12rho((4)/(3)piR^(3))=rhi16pi(R^(3))`
`y_(1)=y_(com)(Co n e)=(H)/(4)=(4R)/(4)=R`
`y_(2)=y_(com)(sphere)=4R+R=5R`
`y_(com)(t o y)=(M_(1)y_(1)+M_(2)y_(2))/(M_(1)+M_(2))`
`=(16rhopiR^(3))/(3)(R)+16rhopi(R^(3))5R`
`16pi rhoR^(3)[(1)/(3)+1]`
`rArr (16 rho pi R^(3)[(R)/(3)+5R])/(16rho phi R^(3)[(1)/(3)+1])=4R`