A U-tube containing a liquid is subjected to a constant horizontal acceleration a₀ . Given that the separation between the vertical limbs is l , determine the difference in the liquid heights across the two arms.

Step-by-step solution

In a frame accelerating horizontally with acceleration a₀ , the free surface of the liquid aligns itself perpendicular to the effective gravity. The angle made by the free surface with the horizontal is given by = a₀ g . From the geometry of the U-tube, if the separation between the vertical limbs is l , the difference in heights h is related to l by = h l . Equating the two expressions for , we get h l = a₀ g . Therefore, h = a₀ l g .