A cylindrical tube, with its base as shown in the figure., is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle θ = 45 ° . P 1 and P 2 are pressures at point 1 and 2 , respectively, located at the base of the tube. Let β = P 1 − P 2 ρ g d , where ρ is density of water, d is the inner diameter of the tube and g is the acceleration

Step-by-step solution

Given, β = P 1 − P 2 ρ g d               . . . 1 Here we can write now, P 3 = P 2 + ρ g − a 2 d P 1 = P 3 − ρ a 2 d P 1 = P 2 + ρ g d − 2 ρ a d P 1 = P 2 + ρ g − a 2 d − ρ a 2 d P 1 − P 2 ρ d g = 1 − 2 a g Compare it with given equation 1 , β = 1 − 2 a g Now check the options, If a = g 2 , β = 0 . If a = g 2 , β = 2 - 1 2 . Option 1 and 3 are correct