0

Guest

Courses New

A U tube is rotated about one of it’s limbs with an angular velocity ω. Find the difference in height H of the liquid (density ρ) level, where diameter of the tube d

A U tube is rotated about one of it’s limbs with an angular velocity ω. Find the  difference in height H of the liquid (density ρ) level, where diameter of the tube d

Question Image
Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
Hello Student,
Please find the answer to your question
Weight of liquid of height H
= πd2 / 4 x H x ρ x g …(i)
Let us consider a mass dm situated at a distance x from A as shown in the figure. The centripetal force required for the mass to rotate = (dm) xω2
∴ The total centripetal force required for the mass of length L to rotate
= \int_{0}^{L} (dm)xω2 where dm = ρ x πd2 / 4 x dx
∴ Total centripetal force
= \int_{0}^{L} (\rho x \tfrac{\pi d^2}{4} x dx)x (xω2)
= ρ x πd2 / 4 x ω2 x L2 / 2 …(ii)
This centripetal force is provided by the weight of liquid of height H.
From (i) and (ii)
πd2 / 4 x H x ρ x g = ρ x πd2 / 4 x ω2 x L2 / 2
H = ω2 L2 / 2g
Thanks
Kevin Nash
askIITians Faculty
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem.
 
 
Weight of liquid of height H
= πd2 / 4 x H x ρ x g …(i)
Let us consider a mass dm situated at a distance x from A as shown
in the figure. The centripetal force required for the mass to rotate = (dm) x ω2
 
∴ The total centripetal force required for the mass of length L to rotate
= ∫(dm) x ω2 where dm = ρ x πd2 / 4 x dx             [limit 0 à L]
 
∴ Total centripetal force
= ∫(ρx πd2/4 xdx)x(xω2)               [limit 0 à L]
= ρ x πd2 / 4 x ω2 x L2 / 2 …(ii)
 
This centripetal force is provided by the weight of liquid of height H.
From (i) and (ii)
πd2 / 4 x H x ρ x g = ρ x πd2 / 4 x ω2 x L2 / 2
H = ω2 L2 / 2g
 
Thanks and regards,
Kushagra
 

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More