A composite rod whose upper half has a density `(rho)/(4)` and lower half has a density of `(3rho)/(2)` is immersed vertically in a liquid of density `rho`. To what length it shoul be immeresed so that centre of buoyancy coincides with centr of mass of the rod ? suppose the length is `(x l)/(14)` Find `x` .

Answer

9

Explanation

A composite …………..
`y_(cm) = ((L)/(2).Axx(3rho)/(2).(L)/(4)+(L)/(2)A.(rho)/(4).(3L)/(4))/((L)/(2)A.(3rho)/(2)+(L)/(2)A.(rho)/(4))=(9L)/(28)`
`implies` height immersed `= 2xx (9L)/(28) = (9L)/(14)`
`implies x = 9`