Question

# 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:

A
aL2g
B
gL2a
C
gLa
D
aLg

Solution

## The correct option is D $$\dfrac {aL}{g}$$Let $$P_1$$ and $$P_2$$ be the pressures at the bottom of the left and right ends of the tube, respectively.Then $$F=(P_1-P_2)A=\rho ghA$$where A is the cross section of the tube.The mass of the liquid in the horizontal portion is$$m=\rho LA$$Now, $$F=ma$$$$\Rightarrow \rho g hA=\rho LAa$$$$\therefore h=\displaystyle\frac {aL}{g}$$Physics

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