First slide

Fluid statics

Question

A metal ball of density 7800 kg/m³ is suspected to have a large number of inner cavities. It weighs 9.8 kg when weighed directly on a balance and 1.5 kg less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately:

Moderate

A

20%
B

30%
C

16%
D

11%

Solution

Volume of metal in ball = $\frac{M}{ρ_{metal}} = \frac{9.8}{7800} = 1.26 \times 10^{- 3} m^{3}$
Total volume of ball $= \frac{Th}{ρ_{w} g} = \frac{1.5 g}{10^{3} \times g} = 1.5 \times 10^{- 3} m^{3}$
Volume of cavity $= 1.5 \times 10^{- 3} - 1.25 \times 10^{- 3} = 0.24 \times 10^{- 3} m^{3}$
Fraction of volume of cavity $= \frac{0.24 \times 10^{- 3}}{1.5 \times 10^{- 3}} \times 100 = 16 %$

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