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A circular tube of uniform cross section...

A circular tube of uniform cross section is filled with two liquids densities `rho_(1)` and `rho_(2)` such that half of each liquid occupies a quarter to volume of the tube. If the line joining the free surfaces of the liquid makes an angle `theta` with horizontal find the value of `theta.`

A

`tan^(-1)((1)/(5))`

B

`tan^(-1)((3)/(2))`

C

`tan^(-1)((2)/(3))`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
A
In equilibrium, pressure of same liquid at same level will be same.
Therefore, `P_(1) =P_(2)`
or `P+(1.5 rho gh_(1)) =P+ (rho gh_(2))`
`(P =` pressure of gas in empty part of the tube)
`:. 1.5 h_(1) =h_(2)`
`1.5 [R cos theta -R sin theta] =(R cos theta +R sin theta)`
or `3cos theta - 3 sin theta =2 cos theta +2 sin theta`
or `5 tan theta =1 theta= tan^(-1) ((1)/(5))`
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Knowledge Check

  • If two liquids of same masses but densities rho_(1) and rho_(2) respectively are mixed, then the density of mixture is given by

    A
    `rho = ( rho_(1) + rho_(2))/( 2)`
    B
    ` rho =( rho_(1) + rho_(2))/( 2 rho_(1) rho_(2))`
    C
    ` rho = (2 rho _(1) rho_(2))/( rho_(1) + rho_(2))`
    D
    ` rho = (rho_(1) rho_(2))/(rho_(1) + rho_(2))`

  • A narrow U-tube placed on a horizontal surface contains two liquids of densities rho_(1) and rho_(2) . The columns of the liquids are indicated in the figure. The ratio (rho_(1))/(rho_(2)) is equal to :

    A
    `(1)/(3)`
    B
    `(2)/(5)`
    C
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    D
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  • The figure represents a U-tube of uniform cross-section filled with two immiscible liquids. One is water with density rho_(w) and the other liquid is of density rho . The liquid interface lies 2 cm above the base. The relation between rho and rho_(w) is .

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    C
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    D
    None of these

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