Let’s break down the problem step by step: --- ## **Given:** - **Diameter** of lamina, \( d = 25\,\text{cm} = 0.25\,\text{m} \) - **Radius** of lamina, \( r = 12.5\,\text{cm} = 0.125\,\text{m} \) - **Depth of top edge** below water surface, \( h_1 = 60\,\text{cm} = 0.60\,\text{m} \) - **Depth of bottom edge** below water surface, \( h_2 = 150\,\text{cm} = 1.50\,\text{m} \) - **Specific weight of water**, \( w = 9800\,\text{N/m}^3 \) --- ## **1. Area of the lamina** \[ A = \pi r^2 = \pi (0.125)^2 = 0.0491\,\text{m}^2 \] --- ## **2. Depth of center of lamina below surface** The lamina lies **vertically** (since edge depths are given), so the **vertical centre** is at \[ h_c = \frac{h_1 + h_2}{2} = \frac{0.60 + 1.50}{2} = 1.05\,\text{m} \] --- ## **3. Total Hydrostatic Force on One Side** Hydrostatic force \( F \) on a submerged plane: \[ F = w \cdot A \cdot h_c \] Plug in the values: \[ F = 9800 \times 0.0491 \times 1.05 \] \[ F = 9800 \times 0.051555 = 504.24\,\text{N} \] --- ## **4. Centre of Pressure** For a vertical plane surface: \[ h_{cp} = h_c + \frac{I_G \sin^2\theta}{A h_c} \] For a **vertical circle**, \( \sin\theta = 1 \). The second moment of area (about horizontal axis through centroid): \[ I_G = \frac{\pi r^4}{4} \] \[ I_G = \frac{\pi}{4} (0.125)^4 = \frac{\pi}{4} \times 0.0002441 = 0.0001918\,\text{m}^4 \] Now, \[ h_{cp} = h_c + \frac{I_G}{A h_c} \] Where \( A = 0.0491\,\text{m}^2 \), \( h_c = 1.05\,\text{m} \): \[ h_{cp} = 1.05 + \frac{0.0001918}{0.0491 \times 1.05} \] \[ 0.0491 \times 1.05 = 0.051555 \] \[ \frac{0.0001918}{0.051555} = 0.00372 \] \[ h_{cp} = 1.05 + 0.00372 = 1.0537\,\text{m} \] --- ## **## Final Answers** ### **(a) Total force due to water on one side of the lamina:** \[ \boxed{504\,\text{N}} \] ### **(b) Vertical distance of centre of pressure below the surface:** \[ \boxed{1.054\,\text{m}} \] --- **Summary Table:** | Parameter | Value | |-----------------------|--------------| | Area, \( A \) | 0.0491 m² | | Depth to centre, \( h_c \) | 1.05 m | | Hydrostatic force, \( F \) | 504 N | | Centre of pressure, \( h_{cp} \) | 1.054 m | Let me know if you want the working shown in more detail!