MHTCET 20 Apr 2026 Shift 2 Paper

Concept:The reaction force of water escaping from a hole is the rate of change of momentum, and for two opposite holes the resultant is the difference of the two forces.Explanation:Let the depths of the two holes below the water surface be $h_1$ and $h_2$.Since the vessel is wide, the efflux speed at depth $h$ is given by Torricelli’s theorem:$$v = \sqrt{2 g h}$$The reaction force for one hole is:$$F = \rho A v^2$$Substituting $v^2 = 2 g h$, we get:$$F = \rho A (2 g h) = 2 \rho A g h$$Thus, forces on the two holes are:$$F_1 = 2 \rho A g h_1, \quad F_2 = 2 \rho A g h_2$$The holes are on opposite sides, so the forces act in opposite directions.Therefore, the resultant force is:$$F_{\text{resultant}} = F_2 - F_1 = 2 \rho A g (h_2 - h_1)$$Given the height difference between the holes is $x$, i.e. $h_2 - h_1 = x$, we get:$$F_{\text{resultant}} = 2 \rho A g x$$Answer:$$\boxed{2 \rho A g x}$$Option B.