A narrow tube completely filled with a liquid is lying on a series of cylinders as shown in the 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

Options

A. `(gH)/(2L)`
B. `(gH)/L`
C. `(2gH)/L`
D. `(gH)/(sqrt2L)`

Answer

A

Explanation

No sliding `implies` pure rolling
Therefore acceleration of the tube `=2a` (since `COM` of the cylinders are moving at a)
`P_(A)=P_(atm)+rho(2a)L` (from the horizontal limb)
Also `P_(A)=P_(atm)+rhogH` (from the vertical limb)
`:. a=(gH)/(2L)`