Fluid Mechanics

JEE Main level, single correct, medium

92 of 192

Question 92 of 192

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises 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 %\%.

Show answer and solution

Answer: (A) +1+1

Capillary height formula: h=2σcos⁡θρgrh = \frac{2\sigma\cos\theta}{\rho g r}
When radius, density, and surface tension each decrease by 1%: r′=0.99rr' = 0.99r, ρ′=0.99ρ\rho' = 0.99\rho, σ′=0.99σ\sigma' = 0.99\sigma
New height: h′=2(0.99σ)cos⁡θ(0.99ρ)g(0.99r)=h⋅0.990.99×0.99=h⋅10.99=h⋅1.0101...h' = \frac{2(0.99\sigma)\cos\theta}{(0.99\rho) g (0.99r)} = h \cdot \frac{0.99}{0.99 \times 0.99} = h \cdot \frac{1}{0.99} = h \cdot 1.0101...
Percentage change: (1.0101−1)×100≈+1.01%(1.0101 - 1) \times 100 \approx +1.01\%, which rounds to +1%.

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Fluid mechanics simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Fluid Mechanics (Surface tension), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.