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JEE Main 202228 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
28 June
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2022 · 28 June · Morning Shift · Physics · Mechanical Properties of Fluids

A water drop of diameter 2cm is broken into 64 equal droplets. The...

A water drop of diameter 2cm2cm is broken into 6464 equal droplets. The surface tension of water is 0.075Nm−10 . 075N{m}^{- 1}. In this process the gain in surface energy will be

Options

  1. A2.8×10−4J2 . 8 \times {10}^{- 4}J
  2. B1.5×10−3J1 . 5 \times {10}^{- 3}J
  3. C1.9×10−4J1 . 9 \times {10}^{- 4}J
  4. D9.4×10−5J9 . 4 \times {10}^{- 5}J

Correct answer

A. 2.8×10−4J2 . 8 \times {10}^{- 4}J

Step-by-step solution

By conserving the total volume 43πR3=64×(43πr3)\dfrac{4}{3}\pi{R}^{3} = 64 \times \left(\dfrac{4}{3}\pi{r}^{3}\right)⇒ R = 4r</p><p>Changeinsurfaceenergyis</p><p></p><p>Change in surface energy is</p><p>\DeltaU = T \times \DeltaA,,= T\left[64 \times 4\pi{r}^{2} - 4\pi{R}^{2}\right]</p><p></p><p>= 4\piT{R}^{2}\left[64 \times \dfrac{1}{16} - 1\right] = 12 \times 3 . 14 \times 0 . 075 \times {10}^{- 4}</p><p></p><p>\approx 2 . 8 \times {10}^{- 4}J

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