Difference in height of the liquid columns in the limbs of a rotating U− tube as shown in the figure is: (Neglect the width of each limb and take g=10m/s2)
A
1m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
0.8m
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
0.5m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
0.6m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B0.8m Let the difference in heights between the liquid columns in the limbs be x′ and atmospheric pressure be p0.
For a rotating fluid, the pressure difference can be given as ΔP=12ρω2x2...(1) where x is the distance between two points in a liquid, measured ⊥ from the axis of rotation. The pressure will increase in a direction away from the axis of rotation. ⇒pB>pA For pressure at A, pA=p0+ρgh2...(2) (due to variation in depth) For pressure at B: pB=pA+12ρω2L2...(3) [∵ we can take AB=x≈L=2m]
Also, pB=p0+ρgh1...(4) (due to variation in depth)
From Eq.(2),(3)&(4), p0+ρgh1=p0+ρgh2+12ρω2L2 ⇒h1−h2=12ω2L2g Then, difference in heights of the liquid in the limbs ⇒x′=h1−h2=12×22×2210 ∴x′=0.8m