AIIMS 2018 Physics Buoyancy MCQ Question

To determine the inner diameter of the hemispherical bowl, we apply the principle of buoyancy, which states that the weight of the liquid displaced must equal the weight of the bowl. Given the outer diameter of 1 m, the volume of the outer hemisphere is $V_{\text{outer}} = \frac{2}{3} \pi \left(\frac{1}{2}\right)^3 = \frac{\pi}{12} \, \text{m}^3$. The weight of the bowl is $W_{\text{bowl}} = V_{\text{outer}} \cdot \text{density}_{\text{bowl}} = \frac{\pi}{12} \times 2 \times 10^4 \, \text{kg/m}^3$. The volume of the liquid displaced must equal this weight divided by the liquid's density $\text{density}_{\text{liquid}} = 1.2 \times 10^3 \, \text{kg/m}^3$.

Solving for the inner diameter, we find that it is approximately 0.98 m, which corresponds to option C. Options A, B, and D do not satisfy the buoyancy condition, as they would result in either insufficient or excessive displacement of liquid, leading to an imbalance in forces acting on the bowl.