Verified Solution • 2025–26 Session moderate

QJEEM23Phdb27: JEE Main 2023 Physics - Class 11 JEEM23Phdb27 Solution: If 1000 droplets of water of surface tension 0.07   N / m…

If 1000 droplets of water of surface tension 0.07 N/m, having same radius 1 mm each, combine to from a single drop. In the process the released surface energy is :-

(Takeπ=227)

Multiple Choice Options

  • A 7.92×10−4 J
  • B 7.92×10−6 J
  • C 8.8×10−5 J
  • D 9.68×10−4 J

Step-by-Step Verified Solution

1000×4π3(1)3=4π3R31000 \times \frac{4 \pi}{3}(1)^{3}=\frac{4 \pi}{3} \mathrm{R}^{3}

R=10 mm\mathrm{R}=10 \mathrm{~mm}

T×1000×4π(10−3)2−T×4π(10×10−3)2=ΔE\mathrm{T} \times 1000 \times 4 \pi\left(10^{-3}\right)^{2}-\mathrm{T} \times 4 \pi\left(10 \times 10^{-3}\right)^{2}=\Delta \mathrm{E}

⇒ ΔE=4×π×7×10−2[1000−100]×10−6\Delta \mathrm{E}=4 \times \pi \times 7 \times 10^{-2}[1000-100] \times 10^{-6}

⇒ ΔE=7.92×10−4 J\Delta \mathrm{E}=7.92 \times 10^{-4} \mathrm{~J}

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