A bent arc shaped sealed glass tube filled with water is accelerated horizontally with acceleration a. A small air bubble inside it is found to be stuck at 1 cm from vertical axis. Neglect surface ten

Question

A bent arc shaped sealed glass tube filled with water is accelerated horizontally with acceleration a. A small air bubble inside it is found to be stuck at 1 cm from vertical axis. Neglect surface tension. What is the acceleration of the tube.

TestHub · Accepted Answer

In the frame of the accelerating tube, effective gravity is $g_{e ff} = g - a$ ; the bubble rests where the wall's normal is along $g_{e ff}$ .

Geometry: bubble stuck 1 cm from the vertical axis on an arc of radius R = 2 cm, so $sin θ = \frac{1}{2}$ , $θ = 3 0^{\circ}$ from vertical.

$tan θ = \frac{a}{g} = tan 3 0^{\circ} = \frac{1}{3}$

$a = \frac{g}{3}$ , directed to the right.

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