A `1m` long rod having uniform area of cross section is made of four materials. The first `0.2 m` is made of iron, the next `0.3m` of lead, the following `0.2m` of aluminium and the remaining part is made of copper. Find the centre of mass of the rod. The densities of iron, lead, aluminium and copper are `7.9xx10^3 kg//m^3,11.4xx10^3 kg//m^3, 2.7 xx 10^3 kg//m^3 "and" 8.9 xx 10^3kg//^3` respectively.

Explanation

mass `(m)`=volume`(V)xx`density `(d)`
`m`=Area`(A)xx`length`(l)xx`density `(d)`
`m=Ald`.

Iron part mass, `m_(1)=Axx0.2xx7.9xx10^(3)=1.58xx10^(3) A`.
Lead part mass `m_(2)=Axx0.3xx11.4xx10^(3)=3.42xx10^(3) A`.
Aluminium part mass,
`m_(3)=Axx0.2xx2.7xx10^(3)=0.54xx10^(3) A`
copper part mass, `m_(1)=Axx0.3xx8.9xx10^(3)=2.67xx10^(3) A` Co-ordinate of lead part of form end "O" of the rod `x_(2)=0.35 m`.
Corrdinate of lead part from end "O" of the rod `x_(2)=0.35 m`
Co-ordinate of aluminium part from end "O" of the rod, `x_(4)=0.84m`
`:.` Centre of mass of the rod,
`x_(CM)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3)+m_(4)x_(4))/(m_(1)+m_(2)+m_(3)+m_(4))`
`rArrx_(CM)=((1.58xx10^(3)xx0.1+3.42xx10^(3)xx0.35+0.54xx10^(3)xx0.6+2.67xx10^(3)xx0.85)A)/((1.58xx10^(3)+3.42xx10^(3)+0.54xx10^(3)+2.67xx10^(3))A)`
`rArrx_(CM)=0.481m` form the end "O" of the rod.