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The uncertainties in the velocities of two particles, A and B an 0.05 and $0.02 {ms}^{- 1}$ respectively. The mass of B is 5 times to that of the mass of A. What is the ratio of uncertainties $\frac{{ΔX}_{A}}{{ΔX}_{B}}$ in their positions ?

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0.25

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Detailed Solution

${ΔX}_{A} \times m \times 0.05 = \frac{h}{4 z} . ...... (i) \begin{array}{l} {ΔX}_{B} \times 5 m \times 0.02 = \frac{h}{4 z} . ...... (ii) \\ ∴ \frac{{ΔX}_{A}}{{ΔX}_{B}} = \frac{5 \times 0.02}{0.05} = 2 \end{array}$

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