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 sawdust 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`=`upthust on the sphere
`(4)/(3)pi(R^3-r^3)rho_1g+(4)/(3)pir^3rho_2g=(4)/(3)piR^3xx1xxg`
`impliesR^3rho_1-r^3rho_1+r^3rho_2=R^3`
`impliesR^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)`
`((R^3-r^3)rho_1)/(r^3rho_2)=((1-rho_2)/(rho_1-1))(rho_1)/(rho_2)`
`implies("mass of concrete")/("mass of saw dust")=((1-0.3)/(2.4-1))xx(2.4)/(0.3)=4`