A ball weighing $10 \mathrm{~g}$ is moving with a velocity of $90 \mathrm{~ms}^{-1}$. If the uncertainty in its velocity is $5 \%$, then the uncertainty in its position is__________ $\times 10^{-33} \mathrm{~m}$. (Rounded off to the nearest integer)
$\left[\right.$ Given : $\left.\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\right]$
$\Delta \mathrm{v}=90 \times \frac{5}{100}$
$=4.5 \mathrm{~m} / \mathrm{s}$
$\Delta \mathrm{v} . \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{m}}$
$\Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{m} \cdot \Delta \mathrm{v}}$
$=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 0.01 \times 4.5}$
$=1.17 \times 10^{-33}$
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