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Q.

A given shaped glass tube having uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in Fig. 12.52. If the tube is rotated with a constant angular velocity ω then :

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a

water levels in both A and B go up

b

water level in section A goes up and that in B comes down

c

water level in section A comes down and that in B it goes up

d

water levels remain same in both sections

answer is C.

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Detailed Solution

ρ=densityA = cross-section area ρghA-ρg(3h-hA-hB)A=(ρAL)ω2L2 2hA+hB-3h=ω2L22g                                     ....(1) ρghB+3h+hA+hBA=ρA(2L)ω22L2 2hB+hA-3h=2ω2L2g                                     .....(2) From eqns.(1) and (2)      hA=h-ω2L23g,hB=h+11ω2L26g ⇒Water level in section B goes up and in section A comes down .
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A given shaped glass tube having uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in Fig. 12.52. If the tube is rotated with a constant angular velocity ω then :