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Q)

When at rest a liquid stands at same level in the tubes shown . But as indicated a height difference of 'h' occurs when the system is given an acceleration towards right. then 'h' equals

$ a)\;\frac{aL}{2a} \\ b)\;\frac{gL}{2a} \\ c)\;\frac{gL}{a} \\d)\;\frac{aL}{g}$

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A)
The water surface while accelerated will lie as shown. with lines of constant pressure parallel to the surface.
 
Take an element of water between lines of constant pressure.
 
$A \Delta P \sin \theta =ma$-------(1)
$A \Delta P \cos \theta =mg$---------(2)
dividing (1) by (2)
$\tan \theta =\large\frac{a}{g}$
$\qquad=\large\frac{h}{L}$
$\therefore h=\large\frac{aL}{g}$
Hence d is the correct answer.

 

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