Question

A bowl of soap water is at rest on a table in the dining compartment of a train, if the acceleration of the train is $g/4$ in forward direction, the angle made by its surface with horizontal is:

• A. ${\tan }^{-1}\left(\frac{1}{2}\right)$
• B. ${\tan }^{-1}\left(\frac{1}{4}\right)$
• C. ${\tan }^{-1}\left(\frac{1}{5}\right)$
• D. ${\tan }^{-1}\left(\frac{1}{3}\right)$

Answer 1

The correct option is B ${\tan }^{-1}\left(\frac{1}{4}\right)$

As the water surface align itself perpendicular to the resultant accelaration as it cannot bear any shear stress,
$tan\theta =\left(\frac{\left(\frac{g}{\alpha }\right)}{g}\right)$
$\Rightarrow \theta ={\tan }^{-1}\left(\frac{1}{4}\right)$