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Physics - Fluid Question with Solution | TestHub

PhysicsFluidPressureMedium2 minQB

PhysicsMediumsingle choice

The gate shown is hinged at H. The 2 m wide gate is normal to the plane of the diagram. Find the force required at A to hold the gate closed. (weight of the gate is negligible):

Options:

Answer:

Solution:

Force on a strip at distance x from H: $d F = ρ g (1 + x sin 3 0^{\circ}) (2 d x) = ρ g (2 + x) d x$

Torque about H: $d τ = ρ g (2 x + x^{2}) d x$

$τ = ρ g [x^{2} + \frac{x ^{3}}{3}]_{0}^{2} = ρ g (4 + \frac{8}{3}) = \frac{20 ρ g}{3}$

$τ = F \times 2 \Rightarrow F = \frac{10 ρ g}{3} = \frac{10 \times 1000 \times 10}{3}$ N

$F = 33.3$ kN

Stream:JEESubject:PhysicsTopic:FluidSubtopic:Pressure

⏱ 2mℹ️ Source: QB

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