Question

A carpenter has constructed a toy as shown in the figure. If density of material of sphere is 12 times that of cone, then the position of centre of mass of the toy is given by (volume of cone = ) ​at a distance 2R from O at a distance 3R from O at a distance 4R from O at a distance 5R from O

Answer 1

If the density of cone is p, then mass of cone = density x volume=p1/3 π(2R)²
= 16/3 π(R)³pThis mass is concentrated at a height from O= h/4 =4R/h = R

Mass of the sphere= m₂= density x volume= 12p x 4/3π(R)³= 16πR³p= m3

This mass is concentrated  at O2, i.e. at a distance of 4R+R=5Rfrom O.Hence centre of mass of whole system will be
Ycm = m1y1 + m2y2/m1 + m2
=mR + 3m(5R)/ m + 3m
= 16mR/ 4m
=4R