question_answer

At rest, a liquid stands at the same level in the tubes. As the system is given an acceleration a towards the right. A height difference h occurs as shown in the figure. The value of h is      

A)  \[\frac{aL}{2g}\]                               

B)  \[\frac{gL}{2a}\]

C)  \[\frac{gL}{a}\]                                 

D)  \[\frac{aL}{g}\]

Correct Answer: D

Solution :

 Newton?s equations are, \[A\Delta p\,\,\sin \theta \,=ma\] and      \[A\Delta p\,\,\cos \theta \,=mg\] By Eqs. (i) and (ii), we get \[\tan \,\theta =\frac{a}{g}=\frac{h}{L}\] or            \[h=\frac{aL}{g}\]