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A container contains two immiscible liquids of density ρ1ρ1 and ρ2(ρ2>ρ1)ρ2(ρ2>ρ1). A capillary of radius rr is inserted in the liquid so that its bottom reaches up to denser liquid. Denser liquid rises in capillary and attains height equal to hh which is also equal to column length of lighter liquid. Assuming zero contact angle find the surface tension of the heavier liquid.

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We will analyse this problem from the reference frame of elava tor. Total buoyant force on the block is
FB=(2 5Vρ2+35 Vρ1)(g+a)FB=(25Vρ 2 +35V ρ1)(g+a)

From the condition of equilibrium
FB=T+Vd(g +a)FB=T +Vd(g+a)
⇒T=F B−V d(g+a)=(g+a)V[ 25ρ 2+3 5ρ 1−d]⇒T=FB -Vd(g+a)=(g+a)V[25 ρ2+35ρ1- d]
=15×10−3[25×1500+35×1000−800]=6N


 
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