wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A container of width 2a is filled with a liquid. A thin wire of mass per unit length μ is gently placed along the middle of the surface as shown in the figure. As a result, the liquid surface is depressed by a distance y. The surface tension of the liquid is σ. Then choose the correct option(s).
[Assume angle of contact between the wire and liquid is acute]


A
σ=μg2cosθ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
σ=μg2sinθ
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
If y<<a, then σ=μga2y
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
If y<<a, then σ=μgay
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct options are
B σ=μg2sinθ
C If y<<a, then σ=μga2y
Consider the FBD of the wire. Surface tension T acts along the liquid surface as shown.


Let l be the length of the wire.
Then, weight of the wire W=μlg
Force due to surface tension f=σl.
Horizontal components fcosθ cancel each other under equilibrium,

In vertical direction, 2fsinθ=W
2σlsinθ=μlg
σ=μg2sinθ

Also, sinθ=ya2+y2
If y<<aa2+y2a [when θ is very small ]
Then, sinθ=ya
σ=μga2y

flag
Suggest Corrections
thumbs-up
6
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Surface Tension
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon