A liquid stands at the plane level in the U-tube when at rest. If areas 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 system is given an acceleration a in horizontal direction towards right as shown?

Options

A. `(g)/(a) (L^(2))/(H)`
B. `(La)/(g)`
C. `(L^(2))/(H)(a)/(g)`
D. `(Lg)/(a)`

Answer

B

Explanation

Change in pressure along horizontal direction, `(dp)/(dX)=rho a`

`therefore Deltap_(AB)=rho aL=rho gh`
`therefore h=(La)/(g)`