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

Solution

Physics sir · 4 steps

Write Jurin's law, then add percentages for what is on top and subtract for what is below.

1. Capillary rise. The height of the liquid column is given by Jurin's law. The contact angle θ and g do not change here.

   h = (2T cos θ)/(rρ g)

2. Small percentage changes. For small changes, the percentage change of h is the percentage change of each quantity in the numerator, minus that of each quantity in the denominator. So (Δ h)/h = (Δ T)/T - (Δ r)/r - (Δ ρ)/ρ.
3. Put in numbers. Each quantity falls by 1%, so (Δ h)/h = (-1) - (-1) - (-1) = +1%. Exact check: h becomes 0.99/(0.99 × 0.99) h = 1.0101 h, which is about 1% more.
4. So. The height of the liquid in the tube increases by about 1%, option (b).

The idea to keep. For a product of powers, add the percentage changes of the factors on top and subtract those below. A decrease in a denominator quantity raises the result.

Answer from the NTA final answer key. Solution by PrepWiser.