A 1m long rod having a constant cross sectional area is made of four materials. The first 0.2m are 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), 2.7xx10^(3)kg//m^(3) and 8.9xx10^(3)kg//m^(3) respectively.

A 1m long rod having a constant cross sectional area is made of four m

1.	A 1m long rod having a constant cross sectional area is made of four materials. The first 0.2m are 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), 2.7xx10^(3)kg//m^(3) and 8.9xx10^(3)kg//m^(3) respectively.
Answer» Solution : mass (m)`=` VOLUME(v) `XX` density (d) m`=` Area(A) `xx` LENGTH(l) `xx` density (d) `m=Ald` Mass of iron part, `m_(1)=Axx0.2xx7.9xx10^(3)` `=1.58xx10^(3)A` Mass of lead part `m_(2)=Axx0.3xx11.4xx10^(3)` `=3.42xx10^(3)A` Mass of aluminium part, `m_(3)=Axx0.2xx2.7xx10^(3)` `=3.42xx10^(3)A` Mass of aluminium part, `m_(3)=Axx0.2xx2.7xx10^(3)` `=0.54xx10^(3)A` Mass of copper part `m_(4)=Axx0.3xx8.9xx10^(3)` `=2.67xx10^(3)A` Co-ordinate of iron part from end ..O.. of the rod `x_(1)=0.1m` Co-ordinate of lead part from end ..O.. of the rod, `x_(2)=0.35m` Co-ordinate of aluminium part from end ..O.. of the rod, `x_(3)=0.6m` Co-ordinate of copper part from end ..O.. of the rod, `x_(4)=0.85m` `:.` Centre of mass of the rod, `X_(c )=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3)+m_(4)x_(4))/(m_(1)+m_(2)+m_(3)+m_(4))` `impliesX_(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)` `impliesX_(cm)=0.481m` from the end "O.. of the rod.