Question

What angle will the free surface of a liquid subtend with the horizontal when the liquid in a container is moving horizontally with constat ac celeration a as shown in fig.

Answer 1

Consider a horizontal liquid cylinder in the liquid, of length L area of cross-section A. Let `h_(1)`and `h_(2)` be the heights of liquid column at the ends of cylinder fro the surface of liquid as shown in fig. for the translatory motion of cylinder with ac celeratoin a.
`F_(1)-F_(2) = ma`
or, `P_(1)A-P_(2)A = AL rho a`
or `(h_(1)rho g - h_(2)rho g)A =AL rho a`
`[ :. P = h rho g]`
or `(h_(1)-h_(2))g = La` or `(h_(1)-h_(2))/(L) = a/g`
From fig, ` tan theta = (h_(1)-h_(2))/(L) = a/g`
so, `theta = tan^(-1) a//g`.