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