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MCQEasyJEE 2026Surface Tension & Capillarity

JEE Physics 2026 Question with Solution

When a part of a straight capillary tube is placed vertically in a liquid, the liquid rises upto certain height hh. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1%1\% each, then the height of the liquid in the tube will change by _____ %\%.

  • A

    −1-1

  • B

    −3-3

  • C

    +1+1

  • D

    +3+3

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: The liquid rises to height hh in a capillary tube. The inner radius rr, density ρ\rho, and surface tension TT each decrease by 1%1\%.

Find: The percentage change in the height of rise.

For capillary rise,

h=2Tcos⁡θρgrh = \frac{2T \cos\theta}{\rho g r}

So,

h∝Tρrh \propto \frac{T}{\rho r}

Using fractional change,

Δhh=ΔTT−Δρρ−Δrr\frac{\Delta h}{h} = \frac{\Delta T}{T} - \frac{\Delta \rho}{\rho} - \frac{\Delta r}{r}

Substitute the given percentage changes:

ΔTT=−1%,Δρρ=−1%,Δrr=−1%\frac{\Delta T}{T} = -1\%, \qquad \frac{\Delta \rho}{\rho} = -1\%, \qquad \frac{\Delta r}{r} = -1\%

Therefore,

Δhh=(−1)−(−1)−(−1)=+1%\frac{\Delta h}{h} = (-1) - (-1) - (-1) = +1\%

Therefore, the height of the liquid column increases by 1%1\%. The correct option is C.

Logarithmic Differentiation Trick

Given: h∝Tρrh \propto \dfrac{T}{\rho r}.

Find: The percentage change in hh when TT, ρ\rho, and rr each decrease by 1%1\%.

When a quantity is proportional to a product and quotient of variables, percentage changes add algebraically according to powers and positions in numerator or denominator.

Here, TT is in the numerator, while ρ\rho and rr are in the denominator.

So directly,

%Δh=%ΔT−%Δρ−%Δr\%\Delta h = \%\Delta T - \%\Delta \rho - \%\Delta r =(−1)−(−1)−(−1)=+1= (-1) - (-1) - (-1) = +1

Hence, the height increases by 1%1\%, so the correct option is C.

Common mistakes

  • Using h∝Trρh \propto Tr\rho instead of h∝Tρrh \propto \dfrac{T}{\rho r}. This is wrong because radius and density are in the denominator in the capillary rise formula. Keep numerator and denominator positions correct before applying percentage changes.

  • Adding all three decreases as −1%−1%−1%=−3%-1\% -1\% -1\% = -3\%. This is wrong because decreases in denominator quantities increase the value of hh. Use signs carefully in the fractional change relation.

  • Ignoring that cos⁡θ\cos\theta, gg, and the factor 22 remain unchanged. This is wrong because only changing quantities contribute to the percentage change. Focus only on TT, ρ\rho, and rr here.

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