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  4. 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 × 10-33 m. (Rounded off to the nearest integer) [Given: . h =6.63 × 10-34 Js ]

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Q. 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 : $\left. h =6.63 \times 10^{-34} Js \right]$

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Solution:

$\Delta v =90 \times \frac{5}{100}$

$=4.5 m / s$

$\Delta v . \Delta x =\frac{ h }{4 \pi m }$

$\Delta x =\frac{ h }{4 \pi m \cdot \Delta v }$

$=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 0.01 \times 4.5}$

$=1.17 \times 10^{-33}$