0

Guest

Courses New

A column of mercury of 10 cm length is contained in the middle of a narrow horizontal 1 m long tube which is closed at both the ends. Both the halves of the tube contain air at a pressure of 76 cm of mercury. By what distance will the column of mercury be displaced if the tube is held vertically

A column of mercury of 10 cm length is contained in the middle of a narrow horizontal 1 m long tube which is closed at both the ends. Both the halves of the tube contain air at a pressure of 76 cm of mercury. By what distance will the column of mercury be displaced if the tube is held vertically

Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
. M is the mid-point of tube AB.
At equilibrium
p1 x A + mg = p2 x A
p1 x A + 10 x A x dHg = p2 x A
⇒ p1 + 10dHg x g = p2
For air present in column AP
p x 45 x A = p1 x (45 + x ) x A
⇒ p1 = 45 / 45 + x x 76 dHg x g …..(ii)
For air present in column QB
p x 45 x A = p2 x (45 – x ) x A
⇒ p2 = 45 / 45 - x x 76 dHg x g (iii)
From (i), (ii) and (iii)
45 x 76 x dHgg / 45 + x + 10 dHg x g = 45 / 45 – x x 76 x dHg x g
⇒ 45 x 76 / 45 + x + 10 = 45 x 76 / 45 – x
x = 2.95 cm.
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

M is the mid-point of tube AB.
At equilibrium
p1 x A + mg = p2 x A
p1 x A + 10 x A x dHg = p2 x A
⇒ p1 + 10dHg x g = p2
For air present in column AP
p x 45 x A = p1 x (45 + x ) x A
⇒ p1 = 45 / 45 + x x 76 dHg x g …..(ii)
For air present in column QB
p x 45 x A = p2 x (45 – x ) x A
⇒ p2 = 45 / 45 - x x 76 dHg x g (iii)
From (i), (ii) and (iii)
45 x 76 x dHgg / 45 + x + 10 dHg x g = 45 / 45 – x x 76 x dHg x g
⇒ 45 x 76 / 45 + x + 10
= 45 x 76 / 45 – x
x = 2.95 cm.

Thanks and Regards

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