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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:
119538_a072c6f2255f40e7a5bac7b7fe2e2062.png


A
aL2g
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B
gL2a
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C
gLa
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D
aLg
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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, $$F=ma$$
$$\Rightarrow \rho g hA=\rho LAa$$
$$\therefore h=\displaystyle\frac {aL}{g}$$
158560_119538_ans.png

Physics

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