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Question

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

A
15 cm
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B
25 cm
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C
20 cm
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D
30 cm
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Solution

## The correct option is A 15 cmLet 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), PC−PA=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), PC−PA=ρg(h2−h1)=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

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