A body weighs 160N in air and 120N when wholly immersed in a liquid of relative density 0.8. The relative density value of the body is (g=10ms-2)

(a) 2.2

(b) 3.2

(c) 1.2

(d) 3.8

W = weight of the body in air = 160 N

ρ' = density of body

V = volume of the body

weight of the body in air is given as

W = ρ' V g eq-1

W' = weight of the body in liquid = 120 N

force of buoyancy is given as

F = W - W'

F = 160 - 120

F = 40 N

ρ = density of liquid = ?

force of buoyancy is given as

F = ρ V g eq-2

dividing eq-1 by eq-2

160/40 = ρ' V g / (ρ V g)

4 = ρ' / (0.8)

ρ' = 3.2

(b) 3.2