A tube of uniform cross-section A is bent to form a circular arc of radius R, forming three quarters of a circle. A liquid of density r is forced through the tube with a linear speed v as shown in figure. The net force exerted by the liquid on the tube is

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$2 A v^{2} ρ$

$\frac{3}{4} A v^{2} ρ$

$\sqrt{2} A v^{2} ρ$

$\frac{1}{2} A v^{2} ρ$

answer is C.

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Detailed Solution

Force is the rate of change of momentum. Initial force is $ρ A v^{2}$ . Final force is also $ρ A v^{2}$ . Since the initial and final forces are perpendicular, net rate of change of momentum is $\sqrt{2} A v^{2} ρ$

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