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…

Question

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 $β = \frac{(P_{1} - P_{2})}{(ρ g d)}$ , where $ρ$ is density of water, $d$ is the inner diameter of the tube and $g$ is the acceleration due to gravity. Which of the following statement(s) is (are) correct?

Aicharya · Accepted Answer

Given, &#946; = P 1 &#8722; P 2 &#961; g d &#160; &#160; &#160; &#160; &#160; &#160; &#160; . . . 1 Here we can write now, P 3 = P 2 + &#961; g &#8722; a 2 d P 1 = P 3 &#8722; &#961; a 2 d P 1 = P 2 + &#961; g d &#8722; 2 &#961; a d P 1 = P 2 + &#961; g &#8722; a 2 d &#8722; &#961; a 2 d P 1 &#8722; P 2 &#961; d g = 1 &#8722; 2 a g Compare it with given equation 1 , &#946; = 1 &#8722; 2 a g Now check the options, If a = g 2 , &#946; = 0 . If a = g 2 , &#946; = 2 - 1 2 . Option 1 and 3 are correct ;

A cylindrical tube, with its base as shown in the figure., is filled with water. It is moving down with a…

Solution