The specific gravities of concrete and sawdust are ρ1 and ρ2 respectively
Given ρ1 = 2.4 and ρ2 = 0.3
According to principle of floatation
Weight of a whole sphere = upthrust on the sphere
\(\begin{array}{l}\frac{4}{3}\pi \left ( R^{3}-r^{3} \right )\rho _{1}g+\frac{4}{3}\pi r^{3}\rho _{2}g=\frac{4}{3}\pi R^{3}\times 1\times g\\\left ( R^{3}-r^{3} \right )\rho _{1}+r^{3}\rho _{2}=R^{3}\\R^{3}\rho _{1}-r^{3}\rho _{1}+r^{3}\rho _{2}=R^{3}\\R^{3}\left ( \rho _{1}-1 \right )=r^{3}\left ( \rho _{1}-\rho _{2} \right )\\\frac{R^{3}}{r^{3}}=\frac{\rho _{1}-\rho _{2}}{\rho _{1}-1}\\\frac{\left ( R^{3}-r^{3} \right )}{r^{3}}=\frac{\rho _{1}-\rho _{2}-\rho _{1}+1}{\rho _{1}-1}\\\frac{\left ( R^{3} -r^{3}\right )\rho _{1}}{r^{3}\rho _{2}}=\left ( \frac{1-\rho _{2}}{\rho _{1}-1} \right )\frac{\rho _{1}}{\rho _{2}}\end{array} \)
(mass of concrete)/(mass of saw-dust) = (1 – 0.3)/(2.4 – 1) x (2.4)/(0.3)
We get,
(mass of concrete)/(mass of saw-dust) = 4
Therefore, the ratio of mass of concrete and the mass of saw-dust is 4
So, the correct option is (d)