A cubical block of co-efficient of linear expansion `alpha_s` is submerged partially inside a liquid of co-efficient of volume expansion `gamma_l`. On increasing the temperature of the system by `DeltaT`, the height of the cube inside the liquid remains unchanged. Find the relation between `alpha_s and gamma_l`.

Answer

A, B

Explanation

Initially, at temperature T
`F_B=mg`
`Axrho_lg=Alrho_bg`

`rArrxrho_l=Lrho_b…..(i)`
At temperature `T+DeltaT`
`F_B'=mg`
`A'xrho'_lg=Alrho_bg [mg remains the same as above]`
Now, `A'=A(1+2alphaDeltaT)`
`rho'_l=rho_l(1-gammaDeltaT)`
`:. A(1+2alphaDeltaT)xrho_l(1-gammaDeltaT)=Lrho_bg`
`rArrxrho_l(1+2alphaDeltaT)(1-gammaDeltaT)=Lrho_b`
`rArrxrho_l(1+2alphaDeltaT)(1-gammaDeltaT)=xrho_l [From(i)]`
`rArr1+2alpha DeltaT-gammaDeltaT=1`
`rArrgamma=2alpha`