A liquid stands at the same level in Utube at rest.If A is the area of cross section and g is the acceleration due to gravity .What will be the difference in height h of the liquid in the two limbs of U tube when th e system is given an acceleration towards right

when the U-tube is at rest, we have the force of gravity acting on it

so,

F = mg

here,

m = density x volume = ρV = ρ(Ah) = ρh(πr²)

thus, we have

F = [ρh(πr²)].g

now, if the U-tube is accelerated towards right

the force exerted on it will be

F' = ma = [ρL(πr²)].a

here,

'a' replaces 'g' and 'L' replaces 'h'

now, by equating the two relations we get

[ρh(πr²)].g = [ρL(πr²)].a

or

hg = La

or

L = hg/a

thus, difference in height will be

dh = h - L = h - (hg/a)

or

dh = h[1 - (g/a)]