Play with Dents
A specially designed container has its bottom inclined at an angle θ=π/3 with the horizontal and a hemispherical dent of radius r=0.1 m is also made in the centre of the bottom concave outside ,convex inside the container.. A liquid density ρ=10 kg/m^3 is filled in the container to a height h=0.1 m above the highest point of the dent. Find an expression for magnitude F of the force of liquid pressure on the dent.Remember that h is above topmost point of the dent.g=10m/s^2. If the answer is (2π√a)/15b find [ ∫x^2 dx] where [.] denotes greatest integer function from x=b to x=a
The answer is 111.
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1 solution
Most times we write the expression for force of water pressure on an infinitesimal portion of the dent and the sum up all these force to find the net resultant. But the procedure is quite complicated to use even after employing integral calculus. let us therefore proceed on another idea. Suppose we consider a portion of water identical to the dent in another container without the dent. This portion is in equilibrium under the action of three forces that are the weight of the potion, normal reaction on its bottom and force of liquid pressure on its hemispherical surface.