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The uncertainties in the velocities of two particles A and B are 0.05 and 0.02 $m . \sec^{- 1}$ . The mass of B is five times to that of mass A. What is the ratio of uncertainties $(\frac{Δ x_{A}}{Δ x_{B}})$ in their positions

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0.25

answer is D.

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Detailed Solution

$Δ x . Δ v = \frac{h}{4 π m} \Rightarrow Δ x α \frac{1}{m . Δ v} \Rightarrow \frac{Δ x_{A}}{Δ x_{B}} = \frac{m_{B} Δ v_{B}}{m_{A} Δ v_{A}} \frac{Δ x_{A}}{Δ x_{B}} = 5 \times \frac{0.02}{0.05} = 2$ =

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