Question

the height h through which of surface tensions and Density d rised un a capillary tube of radius ris given by 2t/rdg.check thw correctness of the relation using the method of dimension​

Answer 1

Answer:

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plez see the attachment given above....☝️☝️

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Answer 2

Answer:

ANSWER

Let the height upto which the liquid rises in the capillary be h

⟹ h=

ρgr

2Scosθ

where r is the radius of the capillary tube

Total upward force due too surface tension F

u

=(Scosθ)2πr

∴ Work done by surface tension W

st

=F

u

h

⟹ W

st

=

ρgr

2Scosθ

×(Scosθ)2πr=

ρg

4πS

2

cos

2

θ

Mass of the liquid rose in the capillary m=ρ(πr

2

h)

Also the centre of mass of the liquid rose by

2

h

.

∴ Work done by gravity force W

g

=−mg

2

h

OR W

g

=−ρ(πr

2

h)×

2

h

=−ρπr

2

g

ρgr

2Scosθ

×(

ρgr

Scosθ

)

⟹ W

g

=−

ρg

2πS

2

cos

2

θ

Heat liberated H=W

st

+W

g

=

ρg

4πS

2

cos

2

θ

−

ρg

2πS

2

cos

2

θ

=

ρg

2πS

2

cos

2

θ