A concrete sphere of radius `R` has cavity of radius `r` which is packed with sawdust. The specific gravities of concrete and sawdust are respectively `2.4 and 0.3` for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of swadust will be

Options

A. 8
B. 4
C. 3
D. zero

Answer

B

Explanation

For flotation
`W = F_B`
Concrete : `sigma_c = 2.4 g//c c`
Sawdust : `sigma_s = 0.3 g//c c`
Water : `rho_omega = 1 g//c c`
`sigma_c((4)/(3) pi R^3 - (4)/(5) pi r^3) g + sigma_s .(4)/(3) pi r^3 g = rho_omega. (4)/(3) pi R^2 g`
`2.4 (R^3 - r^3) + 0.3 r^3 = R^3`
`1.4 R^3 = 2.1 r^2 rArr R^3 = (3)/(2)r^3`
`("Mass of concrete")/("Mass of sawdust") = (m_c)/(m_s) = (sigma_c(R^3 - r^3))/(sigma_s r^3)`
=`(2.4)/(0.3) ((3)/(2) -1) = 4`.
.