Q.53 Determine the total pressure on a circular plate of diameter 2 m, which is placed vertically in water in such a way that the Centre of the plate is 2.5 m below the free surface of the water.
- A77048 NCorrect
- B72058 N
- C70058 N
- D71058 N
Solution
Concept
Total pressure on a submerged plane surface equals specific weight × area × depth of its centroid.
Formula
F = ρ g A h̄
Step-by-step solution
1. Diameter d = 2 m, so A = π d2 / 4 = π × 22 / 4 = 3.1416 m² 2. Depth of centroid h̄ = 2.5 m 3. F = ρ g A h̄ = 1000 × 9.81 × 3.1416 × 2.5 4. F = 77047.6 N ≈ 77048 N
Explanation
The total force on a submerged surface depends on the pressure at its centroid. Pressure at the centroid is ρ g h̄. Multiply this pressure by the plate area to get 77048 N.
Why the other options are wrong
B, C and D are close numbers that come from wrong area, wrong g value or arithmetic error. Only 77048 N matches ρ g A h̄.
Shortcut
9810 × π × 2.5 ≈ 9810 × 7.854 ≈ 77048 N
Common mistake
Using the radius in place of the diameter in A = π d2/4, or using depth of the top edge in place of the centroid depth.
Correct answer: A) 77048 N