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The uncertainties in the velocities of two particles, A and B are 0.05 and $0.02 m s^{- 1}$ respectively. The mass B is five times that of the mass of A. What is the ratio of uncertainties $(Δ x_{A} / Δ x_{B})$ of their positions?

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0.25

answer is A.

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Detailed Solution

$\frac{{(Δ x . m . Δ v)}_{A}}{{(Δ x . m . Δ v)}_{B}} = \frac{h / 4 π}{h / 4 π} = 1 ⊸ \frac{Δ x_{A}}{Δ x_{B}} = \frac{m_{B}}{m_{A}} \times \frac{Δ v_{B}}{Δ v_{A}} = 5 \times \frac{0.02}{0.05} = 2$

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