A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r . If the specific gravity of the shell material is 27 8 with respect to water, the value of r is:

Step-by-step solution

In equilibrium m g = F B 4 3 π R 3 - r 3 ρ 0 g = 4 3 π R 3 ρ w g 1 - r R 3 27 8 ρ w = ρ w 1 - r 3 R 3 = 9 27 1 - 1 3 = r 3 R 3 2 3 = r 3 R 3 r R = 2 3 1 / 3 1 - r 3 R 3 = 8 27 r 3 R 3 = 1 - 8 27 = 19 27 r = 0 . 89