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  4. A metal ball of density 7800 kg / m 3 is suspected to have a large number of 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 :

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Q. A metal ball of density $7800\, kg / m ^{3}$ is suspected to have a large number of 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 :

Solution:

$\therefore $ Volume where metal is present
$=\frac{9.8}{7800}=1.256 \times 10^{-3}$
Buoyancy $=v \rho g=1.5\, g$
$\Rightarrow v \times 1000=1.5$
$v=1.5 \times 10^{-3}$
fraction of volume
$=\frac{1.5 \times 10^{-3}-1.256 \times 10^{-3}}{1.5 \times 10^{-3}} \times 100=16 \%$