A liquid stands at the plane level in the U-tube when at reat. If areals of cross-section of both the limbs are equal, what will be the difference in height h of the two limbs of U-tube, when the sustem is given an acceleration a in horizontal direction towards right as shown?

Options

A. `(aL)/(2g)`
B. `(gL)/(2a)`
C. `(gL)/a`
D. `(aL)/g`

Answer

D

Explanation

Let `P_(1)` and `P_(2)` be the presure at the bottom of the left and right ends of the tube, respectively.
Then `F=(P_(1)-P_(2))A=rhoghA`
Where `A` is the cross section of the tube.
The mass of the liquid in the horizontal portion is
`m=rhoLA`
Now, `F=ma`
`implies rhoghA=rhoLAa`
`:. h=(aL)/g`