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Q.

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

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a

$\frac{2 g H}{L}$

b

$\frac{g H}{L}$

c

$\frac{g H}{2 L}$

d

$\frac{g H}{\sqrt{2} L}$

answer is A.

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Detailed Solution

Question Image
No sliding $\Rightarrow$ pure rolling
Therefore, acceleration of the tube $= 2 a$ (since COM of the cylinders are moving at $' a'$ )
$P_{A} = P_{a t m} + ρ (2 a) L$ (from the horizontal limb)
Also, $P_{A} = P_{a t m} + ρ g H$ (from the vertical limb)
$∴ a = \frac{g H}{2 L}$

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