Question

body P floats in water with half its volume immersed. Another body Q floats in a liquid of density 34th of the density of water with two-third of the volume immersed. The ratio of density of P to that of Q is

Answer 1

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volume = V

density= d

density of water =q = 1000 kg/m3

weight in air = w= Vgd

Buoyant force= (2V/3)qg

density of other liquid =p

volume of body inside water= V- 3V/4= V/4

buoyant force = (V/4)pg

as in both situation the body will float so, 

(2V/3)qg = (V/4)pg

p = 8q/ 3

p = 8 x 1000/3

p= 8 /3 x 10³