A concrete sphere of radius R has cavity of radius r which is packed with saw-dust. The specific gravitites of concrete and sawdust are 2.4 and 0.3 respectively. The sphere floats with its entire volume sub-merged under water. Calculate the ratio of mass of concrete and the mass of saw-dust. (a) 1 (b) 2 (c) 3 (d) 4

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

(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)

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