Two identical cylindrical vessels with their | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $h$ be the common height when the vessels are connected. By the conservation of mass,the total volume of liquid remains constant:$A h_1 + A h_

Vedclass · Accepted Answer

$\frac{1}{4}{({h_1} - {h_2})^2}gA\rho $

Vedclass · Answer

(D) Let $h$ be the common height when the vessels are connected. By the conservation of mass,the total volume of liquid remains constant:$A h_1 + A h_2 = A h + A h = 2Ah$$h = \frac{h_1 + h_2}{2}$The initial potential energy of the system is the sum of the potential energies of the liquid in each vessel. The center of gravity of the liquid in a cylindrical vessel is at half its height:$U_i = (A h_1 ho) g \frac{h_1}{2} + (A h_2 ho) g \frac{h_2}{2} = \frac{1}{2} A ho g (h_1^2 + h_2^2)$After connecting the vessels,the final height in each vessel is $h = \frac{h_1 + h_2}{2}$. The final potential energy of the system is:$U_f = 2 	imes (A h ho) g \frac{h}{2} = A ho g h^2 = A ho g \left( \frac{h_1 + h_2}{2} ight)^2 = \frac{1}{4} A ho g (h_1 + h_2)^2$The work done by gravity is the decrease in potential energy:$W = U_i - U_f = \frac{1}{2} A ho g (h_1^2 + h_2^2) - \frac{1}{4} A ho g (h_1 + h_2)^2$$W = \frac{1}{4} A ho g [2(h_1^2 + h_2^2) - (h_1^2 + h_2^2 + 2h_1 h_2)]$$W = \frac{1}{4} A ho g (h_1^2 + h_2^2 - 2h_1 h_2) = \frac{1}{4} A ho g (h_1 - h_2)^2$

Similar Questions

$A$ cylinder of radius $4 \ cm$ and height $10 \ cm$ is immersed in two liquids as shown. Specific gravity of oil is $0.5$. $2 \ cm$ of the cylinder is in the air. Select the $INCORRECT$ statement. Neglect atmospheric pressure.

$A$ vessel containing water is moving with a constant speed towards the right along a straight horizontal path. Which of the following diagrams represents the surface of the liquid?

Write two parts of fluid mechanics and what studies are made in them?

Vedclass Test Series

Exam Paper Generator

Online Exam Module