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

Let specific gravities of concrete and saw dust are `rho_(1)` and `rho_(2)` respectively. According to principle of floatation weight of whole sphere = upthrust on the sphere
`(4)/(3)rhoi (R^(3)-r^(3))rho_(1)g+(4)/(3) rhoi^(3) rho_(2)g =(4)/(3)rhoi R^(3) xx 1xx g implies R^(3) rho_(1) -r^(3) rho_(1) + r^(3) rho_(2) = R^(3)`
`implies R^(3)(rho_(1)-1) = r^(3)(rho_(1)-rho_(2)) implies (R^(3))/(r^(3))=(rho_(1)-rho_(2))/(rho_(1)-1)`
`implies (R_(3)-r_(3))/(r_(3))=(rho_(1)-rho_(2)-rho_(1)+1)/(rho_(1)-1)implies((R^(3)-r^(3))ro_(1))/(r^(3)rho_(2))=((1-rho_(2))/(rho_(1)-1))(rho_(1))/(rho_(2))`
`("Mass of concrete")/("Mass of saw dust") = ((1-0.3)/(2.4-1)) xx (2.4)/(0.3) =4`