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A U-tube of base length l filled with th...

A `U`-tube of base length `l` filled with the same volume of two liquids of densities `rho` and `2rho` 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

A

`(a)/(2g)l`

B

`(3a)/(2g)l`

C

`(a)/(g)l`

D

`(2a)/(3g)l`

Text Solution

Verified by Experts

The correct Answer is:
B
For the given situation, liquid of density `2rho` should be behind that `rho` from right limb:
`P_(A)=P_(atm)+rhogh`
`P_(B)=P_(A)+rhoa(l)/(2)=P_(atm)+rhogh+rhoa(l)/(2)`
`P_(C)=P_(B)+(2rho)a(l)/(2)=P_(atm)+rhogh+(3)/(2)rhoal....(1)`
But from left limb:
`P_(C)=P_(atm)+(2rho)gh......(2)`
From (1) and (2)
`P_(atm)+rhogh+(3)/(2)rhoal=P_(atm)+2rhoghimpliesh=(3a)/(2g)l`
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