Question

A concrete sphere of radius R has a 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 (a) 8
(b) 4 (C) 3 (d) Zero

Answer 1

Answer:

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Answer 2

Ratio of mass of concrete to mass of sawdust will be 4.

Radius of the sphere = R (Given)

Specific gravity of sawdust 1 = 2.4

Specific gravity of sawdust 2 = 0.3

Let the specific gravity of concrete and saw dust be = ρ1 and ρ2

According to the principle of flotation the weight of a whole sphere = upthrust on the sphere

= 4/3 π ( R³ - r³ )pig + 4/3πr³p2g = 4/3πR³ × 1 × g

= R³rgho - r³p1 + r³p2 = R³

= R³ ( p1 - 1) = r³ ( p1-p2)

= R³/r³ = p2 - p1/p1 -1

= R³ - r³/r³

= 1.03 / 2.4-1 x 2.4 / 0.3

= 4`.

Ratio of mass of concrete to mass of sawdust will be 4.