A U-tube of base length ' λ ' filled with same volume of two liquids of densities ρ and 2 ρ is moving with an acceleration 'a' on the horizontal plane. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height h is given by -
Text Solution
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For the given situation, liquid of density 2 ρ should be behind that of ρ from right limb:
P A = P atm + ρ gh
P a = P A + ρ a 
= P atm + ρ gh + ρ a 
P C = P a + (2 ρ ) a 
= P atm + ρ gh + 
ρ a λ … (1)
But from left limb:
P C = P atm + (2 ρ ) gh … (2)
from (1) and (2)
P atm + ρ gh + 
ρ a λ = P atm + 2 ρ gh
⇒ h = 
λ
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