Q.

When at rest, a liquid stands at the same level in the tubes as shown in the figure. But as indicated, a height difference h occurs when the system is given an acceleration a towards the right. Then h is equal to

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a

aL2g

b

gL2a

c

gLa

d

aLg

answer is D.

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Detailed Solution

Let P1 and P2 be the pressures at the bottom of the left and right ends of the tube, respectively.Then F=P1−P2A=ρghAwhere A is the cross section of the tube.The mass of the liquid in the horizontal portion is m=ρLANow, F=ma⇒ ρghA=ρLAa∴ h=aLg
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When at rest, a liquid stands at the same level in the tubes as shown in the figure. But as indicated, a height difference h occurs when the system is given an acceleration a towards the right. Then h is equal to