Question

A trolley containing a liquid slides down a smooth inclined plane of angle $\alpha$ with the horizontal. Find the angle of inclination $\theta$ of the free surface with the horizontal.

• A. $2\alpha$
• B. $\alpha /2$
• C. $\alpha$
• D. $\alpha /4$

Answer 1

Answer: (C)

$\alpha$

The angle of inclination of the free surface with the horizontal is given as,

$\tan \theta =\frac{a_x}{a_y}$

$\tan \theta =\frac{mg\sin \alpha }{mg\cos \alpha }$

$\tan \theta =\tan \alpha$

$\theta =\alpha$

Thus, the angle of inclination of the free surface with the horizontal is $\alpha$.