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(A) Given mass $m = 10 \, g = 0.01 \, kg$. Velocity $v = 90 \, ms^{-1}$. Uncertainty in velocity $\Delta v = 5 \, \% 	ext{ of } 90 = 90 	imes 0.05 =

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(A) Given mass $m = 10 \, g = 0.01 \, kg$. Velocity $v = 90 \, ms^{-1}$. Uncertainty in velocity $\Delta v = 5 \, \% 	ext{ of } 90 = 90 	imes 0.05 = 4.5 \, ms^{-1}$. According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta v \ge \frac{h}{4 \pi m}$. Substituting the values: $\Delta x = \frac{6.63 	imes 10^{-34}}{4 	imes 3.14 	imes 0.01 	imes 4.5}$. $\Delta x = \frac{6.63 	imes 10^{-34}}{0.5652} \approx 1.17 	imes 10^{-33} \, m$. Rounding to the nearest integer,we get $1 	imes 10^{-33} \, m$.

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

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