Question

A liquid soap bowl rests on a table in the dining car of SHATABDI Express. If the train is accelerating uniformly at rate of $\frac{g}{4}$ in the forward direction, the angle made by the surface of the soap contained in the bowl with the horizontal is $\theta$. Then,

• A. $\theta ={\tan }^{-1}\left(4\right)$
• B. $\theta ={\tan }^{-1}\left(\frac{1}{4}\right)$
• C. $\theta ={\tan }^{-1}\left(16\right)$
• D. $\theta ={\tan }^{-1}\left(\frac{1}{16}\right)$

Answer 1

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

Here, the soap surface aligns itself perpendicular to the resultant acceleration as it cannot bear any shear stress.
$\tan \theta =\frac{ma}{mg}=\frac{a}{g}$
$\tan \theta =\frac{\frac{g}{4}}{g}$
$\tan \theta =\frac{1}{4}$
$\Rightarrow \theta ={\tan }^{-1}\left(\frac{1}{4}\right)$