Question

A solid weighs 200N in air, 150N in water and 170N in a liquid. Find relative density of solid, relative density of liquid and density of liquid in Sl system.

Answer 1

`\rho_(s) = 4`

`\rho_(l) = 0.6`

`\rho{liq} = 600 kg/m^(3)`

Given:

Weight of solid in air,
`w_(sa) = 200 N`

Weight of solid in water,
`w_(sw) = 150 N`

Weight of solid in liquid,
`w_(sl) = 170 N`

Solution:

Calculation of:

1. Relative density of solid,
`\rho_(s)`

`\rho_(s) = (w_(sa))/(w_(sa) - w_(sw))`

`\rho_(s) = (200)/(200 - 150) = 4`

2. Relative density of liquid,
`\rho_(l)`

`\rho_(l) = (w_(sa) - w_(sl))/(w_(sa) - w_(sw))`

`\rho_(l) = (200 - 170)/(200 - 150) = 0.6`

3. Density of liquid in S.I units:

Also, we know:

`\rho{l} = (\rho_(liq))/(\rho_(w))`

where

`= {\rho_(liq)}` = density of liquid

`= {\rho_(w)} = 1000 kg/m^(3)` = density of water

Now, from the above formula:

`0.6 = (\rho_(liq))/(1000)`

`\rho{liq} = 600 kg/m^(3)`