CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

A solid cube is first floating in a liquid. The coefficient of linear expansion of the cube is α and the coefficient of volume expansion of the liquid is γ. On increasing the temperature of the (liquid + cube) system, the cube will sink if


A
γ=3α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
γ>3α
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
γ<3α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
γ=2α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B γ>3α
From thermal expansion of a liquid, we can say that,
γreal=γapp+γcube
Let the linear expansion of the cube be α
Then, volume expansion coefficient of cube (γcube)=3α .......(1)
γreal=γapp+3α ........(2)
Given,
Initially cube is floating in the liquid.
Density of cube is less than the density of liquid i.e ρcube<ρliquid
Cube will sink if density of cube is greater than the density of liquid i.e ρcube>ρliquid .....(3)

From the formula of variation of density with temperature
ρ=ρ(1γΔT), we can write,
For cube: ρcube=ρcube(1γcube ΔT) ........(4)
For liquid : ρliquid=ρliquid(1γreal ΔT) ........(5)
Applying condition (3) and substituting (4) and (5), we get
ρcube(1γcube ΔT)>ρliquid(1γreal ΔT)
Since ρcube<ρliquid,
1γcube ΔT>1γreal ΔT
γreal>γcube
i.e γreal>3α
[using (1)]
Hence, option (b) is the correct answer.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon