CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Difference in height between the liquid columns in the vertical arms is - [Take g=10 m/s2]


A
15 cm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
25 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
20 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
30 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 15 cm
Let the difference in height between the liquid columns in the vertical arms be x and atmosphere pressure be P0.
(l2>l1), the centrifugal force acting on the right limb will be greater, thus a higher liquid rise is obtained in this limb.


In case of rotating fluid, the pressure difference is ΔP=12ρω2x2, with pressure increasing opposite to the direction of centripetal acceleration.

For pressure at A,
PA=PB+12ρω2l21
PA=PB+12ρ×22×(0.5)2
Or, PA=PB+ρ2 ...(1)
For pressure at C,
PC=PB+12ρω2l22
PA=PB+12ρ(2)2(1)2
PC=PB+2ρ ...(2)
On subtracting Eq.(1) from (2),
PCPA=3ρ2 ...(3)

For pressure variation due to vertical height for both limbs,
PA=P0+ρgh1 ...(4)
Similarly
PC=P0+ρgh2 ...(5)

On subtracting Eq.(4) from (5),
PCPA=ρg(h2h1)=ρgx ...(6)
On comparing Eq.(3) and (6), we get
3ρ2=ρgx
x=32g m
x=15 cm
Difference in the heights of the liquid columns in the limbs is 15 cm

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon