Question

) Downward force due to gravity, When liquid having density d is in a column of radius ‘r’ set up at height ‘h’ is balanced by upward thrust due to surface tension . Hence

a. 2 π r ɣ = mg

b. 2 r ɣ = mhdg

c. 2 r ɣ = π hdg

d. 2m ɣ = rhdg

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Answer 1

Explanation:

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

⟹    h=ρgr2Scosθ                    where  r is the radius of the capillary tube

Total upward force due too surface tension     Fu=(Scosθ)2πr

∴  Work done by surface tension       Wst=Fuh

⟹    Wst=ρgr2Scosθ×(Scosθ)2πr=ρg4πS2cos2θ

Mass of the liquid rose in the capillary       m=ρ(πr2h)

Also the centre of mass of the liquid rose by  2h.

∴   Work done by gravity force       Wg=−mg2h

OR     Wg=−ρ(πr2h)×2h=−ρπr2gρgr2Scosθ×(ρgrScosθ)

⟹   Wg=−ρg2πS2cos