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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3sc217

8.0 mL of oil is dispersed in water as identical spherical droplets of radius 2.0 micrometre (use $π = 3.14$ ). Select the correct statement(s).

AThe total oil-water interfacial area is 12 $m^{2}$ .
BReducing the radius to 1.0 micrometre doubles the total interfacial area.
CThe number of droplets is about $2.4 \times 1 0^{11}$ .
DHalving the radius leaves the number of droplets unchanged.

Answer: A, B, C

Area

= 3 V / r = 3 \times 8.0 \times 1 0^{- 6} / (2.0 \times 1 0^{- 6}) = 12 m^{2}

, and area

\propto 1/ r

, so it doubles when

r

is halved. Number

= V / (\frac{4}{3} π r^{3}) = 2.39 e + 11

, i.e. about

2.4 \times 1 0^{11}

. Since

n \propto 1/ r^{3}

, halving the radius gives 8 times as many droplets, so statement 4 is wrong.

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