A hemispherical bowl just floats without sinking in a liquid of density 1.2 × 10 3 kg m - 3 . If the outer diameter and the density of the bowl are 1 m and 2 × 10 4 kg m - 3 respectively, then the inner diameter of the bowl will be

Step-by-step solution

Weight of the bowl = mg = V ρ g = 2 3 π [ ( D 2 ) 3 - ( d 2 ) 3 ] ρ g , where D is the outer diameter, d is the inner diameter and ρ is the density of bowl. Weight of the liquid displaced by the bowl =V ' σ g = 2 3 π D 2 3 σ g , where σ is the density of the liquid. For the flotation, 2 3 π ( D 2 ) 3 σ g = 2 3 π [ ( D 2 ) 3 - ( d 2 ) 3 ] ρ g By solving we get d = 0.98   m