Question

A narrow tube completely filled with a liquid is lying on a series of cylinders as shown in figure. Assuming no sliding between any surfaces, the value of acceleration of the cylinders for which liquid will not come out of the tube from anywhere is given by:

• A. $\frac{gH}{2L}$
• B. $\frac{gH}{L}$
• C. $\frac{2gH}{L}$
• D. $\frac{gH}{\sqrt{2}L}$

Answer 1

The correct option is B $\frac{gH}{L}$

For the liquid not to be flow, pressure difference between ends should be zero.

$\Rightarrow$ Pressure due to horizontal acceleration $\left(a\right)$ balances pressure due to gravity $\left(g\right)$

$\Delta P=\rho gH$ $=\rho aL$

$\Rightarrow a=\frac{gH}{L}$