First slide

Fluid statics

Question

A metallic sphere with an internal cavity weighs 40 gwt in air and 20 gwt in water. If the density of the material with cavity be 8 g per ${cm}^{3}$ then the volume of cavity is:

Moderate

A

zero
B

15 ${cm}^{3}$
C

5 ${cm}^{3}$
D

20 ${cm}^{3}$

Solution

Weigth of sphere in air = 40 gwt
Weight of sphere in water = 20 gwt
Loss in weight = (40-20) gf = 20 gwt
Weight of water displaced = loss in weight = 20 gwt
Mass of water displaced = 20 g
Volume of water displaced = 20 ${cm}^{3}$
Actual volume of sphere = volume of water displaced
= 20 ${cm}^{3}$
Volume of material in the sphere = $\frac{40}{8} = 5 {cm}^{3}$
Volume of cavity = (20-5) = 15 ${cm}^{3}$

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