A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The relative densities of concrete and sawdust are 2.4 and 0.3 respectively. For this sphere to float with its entire volume submerged under water, the ratio of the mass of concrete to the mass of sawdust will be

Step-by-step solution

4 3 π r 3 × 0 . 3 g + 4 3 π R 3 - r 3 × 2.4 g = 4 3 π R 3 × 1 × g o r 0.3 r 3 + 2.4 R 3 - 2.4 r 3 = R 3 o r 1.4 R 3 = 2.1 r 3 o r R 3 r 3 = 3 2 o r R 3 - r 3 r 3 = 1 2 Now, m a s s o f c o n c r e t e m a s s o f s a w - d u s t = 4 3 π R 3 - r 3 2.4 4 3 π r 3 × 0.3 = 1 2 × 8 = 4