question_answer

An open vessel containing water is given a constant acceleration a in the horizontal direction. Then, the free surface of water gets sloped with the horizontal at an angle \[\theta \] given by:

A)  \[\theta ={{\tan }^{-1}}\left( \frac{a}{g} \right)\]              

B)  \[\theta ={{\tan }^{-1}}\left( \frac{g}{a} \right)\]

C)  \[\theta ={{\sin }^{-1}}\left( \frac{a}{g} \right)\]              

D)  \[\theta ={{\cos }^{-1}}\left( \frac{g}{a} \right)\]

Correct Answer: A

Solution :

From the figure \[\tan \theta =\frac{ma}{mg}=\frac{a}{g}\]                 \[\Rightarrow \]               \[\theta ={{\tan }^{-1}}\left( \frac{a}{g} \right)\]