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A cube of coefficient of linear expansio...

A cube of coefficient of linear expansion `alpha` is floating in a bath containing a liquid of coefficient of volume expansion `gamma_(l)`. When the temperature is raised by `DeltaT`, the depth upto which the cube is submerged in the liquid remains the same. Find relation between `alpha` and `gamma_(l)`

A

`gamma = 3alpha_(s)`

B

`gamma_(1) = 3alpha_(s) //2`

C

`gamma_(1) = 2alpha_(s)`

D

`gamma_(1) = alpha_(s) //2`

Text Solution

Verified by Experts

The correct Answer is:
C
`mg = l_(1)^(2)drho_(1)g`
`mg = l_(2)^(2)drho_(2)g`
`l_(2) = l_(1)(1 + alpha_(s)Deltat) , rho_(2) = (rho_(1))/(1 + gamma_(1)Deltat)`
`l_(1)^(2)d rho_(1)g = l_(1)^(2)(1+ alpha_(s)Deltat^(2))(rho_(1)dg)/(1 + r_(2)Deltat)`
`1 + gamma_(1)Deltat = (1 + alpha_(s)Deltat)^(2)`
`gamma_(1) cong 2alpha_(s)`
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