When at rest, a liquid stands at the same level in the tubes as shown in the figure. But indicated…..

Q: When at rest, a liquid stands at the same level in the tubes as shown in the figure. But indicated, a height difference h occurs when the system is given an acceleration a towards the right. Then h is equal to

Numerical

(a) $ \displaystyle \frac{a L}{2 g}$

(b) $ \displaystyle \frac{g L}{2 a}$

(c) $ \displaystyle \frac{g L}{ a }$

(d) $ \displaystyle \frac{a L}{ g}$

Ans: (d)

Sol: Let A =  area of cross-section of the tube

ρ =  density of the liquid

Mass of liquid in horizontal section is

m = A L ρ

Net Force = Mass × acceleration

$\large (\rho g h)A = A L \rho \times a $

$\large h = \frac{a L}{g} $

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