Science Questions and Answers

Start Your Free Trial

A body weighs 40N in air,36.4N in a liquid and 36N in water.calculate the relative density of the liquid

Expert Answers info

Jorge Bayard eNotes educator | Certified Educator

calendarEducator since 2014

write123 answers

starTop subjects are Science and Math

The relative density (ρr) is the relationship between the density of a substance (ρs), with another density which is taken as reference. For liquids and solids, it is taken as reference the density of water (ρH2O).

ρr = ρ(s)/ρ(H2O)

Another thing is that the weight (W) of a body in a liquid, is the difference between its weight in air and the buoyancy force exerted by the liquid on the body.

W = W(air) – ρgV

ρgV   →   Buoyant force of the liquid. 

Where:

ρ   →   Density of the liquid.

g   →   Acceleration of gravity.

V   →  Volume of the body.

So, according to the data, we can write:

W(liq) = W(air) – ρ(liq) gV   →   ρ(liq) gV = W(air) – W(liq) = 40 – 36.4 = 3.6 N

ρ(liq) = 3.6/gV

W(H2O) = W(air) – ρ(H2O) gV   →   ρ(H2O) gV = W(air) – W(H2O) = 40 – 36 = 4 N

ρ(H2O) = 4/gV

Applying equation (1), we have:

ρr = ρ(liq)/ρ(H2O) = (3.6/gV)/(4/gV) = 3.6/4

ρr = 0.9

The relative density of the liquid is ρr = 0.9

check Approved by eNotes Editorial

Lupe Tanner, Ph.D. eNotes educator | Certified Educator

briefcaseCollege Professor

bookPh.D. from Oregon State University


calendarEducator since 2015

write3,394 answers

starTop subjects are Science, Math, and Business

Relative density of the liquid is its density relative to the water and it can be calculated as a ratio of weight loss of body in liquid to weight loss of body in water. 

This can also be written as,

relative density of liquid = `(m_1-m_2)/(m_1-m_3)`

where, m1: weight of body in air

m2: weight of body in liquid and m3 is weight of body in water

hence, relative density of liquid = (40-36.4)/(40-36) = 3.6/4 = 0.9

check Approved by eNotes Editorial