Play with Dents

Level pending

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

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