Question

A body is immersed in a liquid of relative density 2.6. It is found that the weight of the body in the liquid is two-thirds of its weight in air. Calculate the density of the body ?

Answer 1

Let `rho` be the density of the body and `V_(1)` its volume, then according to Archimedes principle
`V_(1)rho g-V_(1)rho_(1)g=(2)/(3)V_(1)rhog`
`(rho_(1)`=density of the liquid)
`therefore V_(1)rho g-v_(1)rhog-(2)/(3)V_(1)rho g`
`implies rho=3rho_(1)=3xx2.6xx10^(3) kg m^(-3)`
`=7.8xx103 kg m^(-3)`
Density of the body is `7.8xx103 kg m^(-3)`