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 ....... $\%$
Diffcult
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$9.8=7800\left(\mathrm{v}_{\mathrm{s}}\right){\mathrm{g}}$
$1.5=1000\left(\mathrm{v}_{\mathrm{s}}+\mathrm{v}_{\mathrm{e}}\right) \mathrm{g}$
$\frac{v_{s}}{v_{s}+v_{c}}=\frac{9.8}{1.5} \times \frac{10}{78}=83.76 \%$
$\frac{\mathrm{v}_{\mathrm{e}}}{\mathrm{v}_{\mathrm{s}}+\mathrm{v}_{\mathrm{c}}} \simeq 16 \%$
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