A U-tube containing a liquid is accelerated horizontally with a constant acceleration `a_0`. If the separation between the vertical limbs is l find the difference in the heights of the liquid in the two arms.

Options

A. `ad//g`
B. `2da//g`
C. `da//2g`
D. `d tan (a//g)`

Answer

A

Explanation

Let `A` : area of cross-section of tube
`rho` : density of the liquid
Mass of the liquid in `AB = m = rho Ad`
`P_A = rho gh_2, P_B = rho gh_1`
Net force = mass `xx` acceleration
`(P_A - P_B) A = ma = rho A d a`
`rho g (h_2 - h_1) A = rho A da`
`(h_2 - h_1) g = da`
`h_2 - h_1 = (da)/(g)`.
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