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A hinged gate of length 5 m, inclined at 30° with the horizontal and with water mass on its left, is shown in figure below. Density of water is 1000 kg/m³. The minimum mass of the gate in kg per unit width (perpendicular to the plane of paper), required to keep it closed 5 m
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- 5000
- 6600
- 7546
- 9623
Correct Option: D
Given data
l = 5 m
θ = 30°
ρ = 1000 kg/m³
h = 2.5sin30° = 1.25m 
A = bl = 1 × 5 = 5 m²
| IG = | = | = 10.41 m4 | ||
| 12 | 12 |
F = ρgAh = 1000 × 9.81 × 5 × 1.25 = 61312.5N
| h* = h + | . sin² θ | |
| Ah |
| = 1.25 + | . sin² 30° = 1.67 m | |
| 5 × 1.25 |
Taking moment about hinge
| F = | = W × 2.5 × cos30° | |
| sin 30° |
| 61312.5 × | = Mg × 2.165 | |
| 0.5 |
M = 9623kg
