1.A U-tube filled with water accelerates horizontally with acceleration $a$. Find the height difference $\Delta h$ between the liquid levels in the two vertical limbs separated by distance $L$.
Sol: Effective surface inclination $\tan\theta = \frac{a}{g} = \frac{\Delta h}{L} \implies \Delta h = \frac{a L}{g}$.
2.Two soap bubbles of radii $r_1$ and $r_2$ ($r_1 > r_2$) coalesce under isothermal conditions to form a common interface. Find radius of curvature of common surface.
Sol: Excess pressure difference $\Delta P = \frac{4S}{r_2} - \frac{4S}{r_1} = \frac{4S}{R_c} \implies \frac{1}{R_c} = \frac{1}{r_2} - \frac{1}{r_1} \implies R_c = \frac{r_1 r_2}{r_1 - r_2}$.
