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A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N m⁻¹. In this process the gain in surface energy will be

Asked in JEE Main 28th June 2nd Shift 2022 · Splitting a drop

• (1) 2.8×10⁻⁴ J
• (2) 1.5×10⁻³ J
• (3) 1.9×10⁻⁴ J
• (4) 9.4×10⁻⁵ J

Step-by-step solution

Why the other options are wrong

• (2) comes from makes both slips at once — the diameter 2 cm used as the radius and the -1 dropped: 4π(0.02)²(0.075)(4)=1.51×10⁻³ J.
• (3) comes from uses n^1/3-1=2, the value belonging to 27 drops, in place of 4-1=3: 9.42×10⁻⁵×2=1.9×10⁻⁴ J.
• (4) comes from is the parent drop's own surface energy 4π R²T=9.42×10⁻⁵ J, reported without the factor (n^1/3-1) that turns it into the gain.

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