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JEE Main 2024 (6 Apr, Shift 1) · Splitting & Merging of Drops

Splitting & Merging of Drops question from JEE Main 2024 (6 Apr, Shift 1)

Q25JEE Main 2024 · 6 APR · SHIFT 1Easy

Splitting & Merging of Drops

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is 10x\frac{10}{x}. The value of xx is ________.

Numerical answer type. Work it out, then open the answer.

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Answer: 1

  1. Volume conserved: 1000 r3=R3⇒R=10r1000\, r^3 = R^3 \Rightarrow R = 10r.
  2. Energy of droplets =1000⋅4πr2T= 1000 \cdot 4\pi r^2 T; energy of big drop =4π(10r)2T=100⋅4πr2T= 4\pi (10r)^2 T = 100 \cdot 4\pi r^2 T.
  3. Ratio =1000100=10=10x= \frac{1000}{100} = 10 = \frac{10}{x}
  4. So x=1x = 1.
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