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  • A ball weighing 10g is moving with velocity of 90ms-1. If the uncertainty in its velocity is 5%, the uncertainty in its position is _______<img alt="\times 10^{-33}m" src="https://entrancecorner.codecogs.com/gif.latex?%5Ctimes%2010%5E%7B-33%

A ball weighing 10g is moving with velocity of 90ms-1. If the uncertainty in its velocity is 5%, the uncertainty in its position is _______\times 10^{-33}m. (Rounded off to the nearest integer) [Given : h = 6.63 \times 10^{-34}Js]
Option: 1 1
Option: 2 -
Option: 3 -
Option: 4 -

Answers (1)

best_answer

\begin{array}{l} m=10 g=10^{-2} \mathrm{Kg} \\ v=90 \mathrm{~m} / \mathrm{sec} \end{array}

\Delta \mathrm{v}=\mathrm{v} \times 5 \%=90 \times \frac{5}{100}=4.5 \mathrm{~m} / \mathrm{sec}

\mathrm{m} \cdot \Delta \mathrm{v} \cdot \Delta \mathrm{x} \geq \frac{\mathrm{h}}{4 \pi}

10^{-2} \times 4.5 \times \Delta x \geq \frac{6.63 \times 3 \times 10^{-34}}{4 \times \frac{22}{7}}

\Delta \mathrm{x} \geq \frac{6.63 \times 7 \times 2 \times 10^{-34}}{9 \times 4 \times 22 \times 10^{-2}}

\begin{array}{l} \Delta x \geq 1.17 \times 10^{-33}=x \times 10^{-33} \\\\ \Rightarrow x=1.17 \simeq 1 \end{array}

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