Dual Nature of Matter

JEE Main level, single correct, medium

4 of 200

Question 4 of 200

An oil drop of the radius 2mm2mm with a density 3g3g cm−3{cm}^{-3} is held stationary under a constant electric field 3.55×105Vm−13.55\times {10}^{5}V{m}^{-1} in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (considerg=9.81ms−2)\left(\text{consider}g=9.81m{s}^{-2}\right).

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Answer: (B) 1.73×10101.73\times {10}^{10}

qE=MgqE=Mg⇒neE=ρ(43πr3)×g\Rightarrow neE=\rho \left(\dfrac{4}{3}\pi {r}^{3}\right)\times g
⇒n×1.6×10−19×3.55×105\Rightarrow n\times 1.6\times {10}^{-19}\times 3.55\times {10}^{5}=3×103×43×π×(2×10−3)3×9.81=3\times {10}^{3}\times \dfrac{4}{3}\times \pi \times {\left(2\times {10}^{-3}\right)}^{3}\times 9.81
⇒n=173×10(3−9−5+19)\Rightarrow n=173\times {10}^{(3-9-5+19)}⇒n=1.73×1010\Rightarrow n=1.73\times {10}^{10}.

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