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Properties of Matter question

2022 · 30 Jun · Shift 1 · Q62
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Properties of Matter question

2022 · 30 Jun · Shift 1 · Q62

JEE MainPhysicsProperties of MatterNumerical+4 / −1
The excess pressure inside a liquid drop is 500 Nm −-− 2. If the radius of the drop is 2 mm, the surface tension of liquid is x ×\times× 10 −-− 3 Nm −-− 1. The value of x is ‾\underline{\hspace{2cm}}​.
Numerical answer
View written solutionFree

Correct answer: 500

  1. Use the formula for excess pressure in a liquid drop

For a liquid drop, the excess pressure is

ΔP=2Tr\Delta P = \frac{2T}{r}ΔP=r2T​

where:

  • ΔP\Delta PΔP = excess pressure
  • TTT = surface tension
  • rrr = radius of the drop
  1. Substitute the given values

Given:

ΔP=500 N m−2,r=2 mm=2×10−3 m\Delta P = 500\ \text{N m}^{-2}, \qquad r = 2\ \text{mm} = 2 \times 10^{-3}\ \text{m}ΔP=500 N m−2,r=2 mm=2×10−3 m

So,

500=2T2×10−3500 = \frac{2T}{2 \times 10^{-3}}500=2×10−32T​
  1. Solve for surface tension TTT
500=2T2×10−3=T10−3500 = \frac{2T}{2 \times 10^{-3}} = \frac{T}{10^{-3}}500=2×10−32T​=10−3T​

Hence,

T=500×10−3 N m−1T = 500 \times 10^{-3}\ \text{N m}^{-1}T=500×10−3 N m−1
  1. Compare with the required form

Given that

T=x×10−3 N m−1T = x \times 10^{-3}\ \text{N m}^{-1}T=x×10−3 N m−1

Comparing,

x=500x = 500x=500
  1. Final Answer
500\boxed{500}500​
  1. Comparison with stored correct answer

Stored correct answer = 500500500.

Our derived answer also is 500500500, so they agree.

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