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 atowards the right. Then h is equal to

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 ism=ρLA Now, F=ma⇒ ρghA=ρLAa⇒h=aLg