A body floats in water with one-third of its volumeabove the surface o

1.	A body floats in water with one-third of its volumeabove the surface of water. If it is placed in some oil,it floats with half of its volume above the oil surface.Then, specific gravity of the oil is
Answer» Let the total volume of the body be V. Its density be ‘d’ and the density of water be q = 1000 kg/m3 Weight of the body in air, W = Vdg Volume of body inside water = V – V/3 = 2V/3 So, buoyant force is = (2V/3)qg Let the density of the oil be ‘p’ and the volume of body inside that liquid is = V – V/2 = V/2 Again the buoyant force is = (V/2)pg Since, in both case the body floats so, (2V/3)qg = (V/2)pg => p = 4q/3 Hence specific gravity = 4/3

A body floats in water with one-third of its volumeabove the surface of water. If it is placed in some oil,it floats with half of its volume above the oil surface.Then, specific gravity of the oil is

Answer»

Let the total volume of the body be V. Its density be ‘d’ and the density of water be q = 1000 kg/m3

Weight of the body in air, W = Vdg

Volume of body inside water = V – V/3 = 2V/3

So, buoyant force is = (2V/3)qg

Let the density of the oil be ‘p’ and the volume of body inside that liquid is = V – V/2 = V/2

Again the buoyant force is = (V/2)pg

Since, in both case the body floats so,

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

=> p = 4q/3

Hence specific gravity = 4/3