InterviewSolution
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InterviewSolution
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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 |
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Answer» Correct Answer - 4 Let R be the radius of the whole sphere. Let `rho_1, rho_2` be the specific gravity of concrete and saw dust respectively. Ac cording to principle of floatation, weight of whole sphere = upthrust `(4)/(3) pi (R^3 - r^3) rho_1 +(4)/(3) pi r^3 rho_2 = (4)/(3)pi R^3 xx1` or `R^3 rho_1 - r^3 rho_1 + r^3 rho_2 = R^3` or `R^3 (rho_1 - 1) =r^3(rho_1- rho_2)` or `(R^3)/(r^3) = ((rho_1 -rho_2))/((rho_1 - rho_1))` `or (R^3 - r^3)/(r^3) = ((rho_1 - rho_2) - (rho_1 - 1))/((rho_1 - 1))` or `((R^3 - r^3) rho_1)/(r^3 rho_2) = ((1 - rho_2)/(rho_1 - 1))xx (rho_1)/(rho_2)` `:.("Mass of concrete")/("Mass of saw dust") = ((4)/(3)pi (R^3 - r^3)rho_1)/((4)/(3)pi r^3 rho_2)` `=((R^3 - r^3)rho_1)/(r^3 rho_2) = ((1 - rho_2) rho_1)/((rho_1 - 1)rho_2)` `=((1 -0.3)/(2.4 - 1))xx(2.4)/(0.3) = 4` |
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