A `U`- tube shown in Fig. containing two liquids of specific gravities `rho_(1)` and `rho_(2)` is given an acceleration `a` in the horizontal direction. What is the ratio `rho_(1) : rho_(2)`?

Explanation

Let `A` and `B` the two free liquid levels in the two limbs. If `P_(0)` be the atmosphere pressre, then starting from point `A` and reacing point `B` through the tube, we have
`P_(0)+h_(1)rho_(1)g-lrho_(2)g=P_(0)`
`impliesh_(1)rho_(1)g=lrho_(2)a+h_(2)rho_(2)g=rho_(2)(la+h_(2)g)`
`implies(rho_(1))/(rho_(2))=(la+h_(2)g)/(h_(1)g)`