A table-tennis ball has a mass of 10 g and a | vedclass

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Question

(A) Given: Mass $m = 10 \ g = 0.01 \ kg$,Speed $v = 90 \ m/s$. Accuracy in speed is $4\%$,so uncertainty in speed $\Delta v = \frac{4}{100} 	imes 90

Vedclass · Accepted Answer

$3.6 \ m/s, 1.46 	imes 10^{-33} \ m$

Vedclass · Answer

(A) Given: Mass $m = 10 \ g = 0.01 \ kg$,Speed $v = 90 \ m/s$. Accuracy in speed is $4\%$,so uncertainty in speed $\Delta v = \frac{4}{100} 	imes 90 = 3.6 \ m/s$. According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta p \ge \frac{h}{4 \pi}$. Since $\Delta p = m \cdot \Delta v$,we have $\Delta x \ge \frac{h}{4 \pi m \Delta v}$. Substituting the values: $\Delta x \ge \frac{6.626 	imes 10^{-34} \ J \cdot s}{4 	imes 3.14 	imes 0.01 \ kg 	imes 3.6 \ m/s}$. $\Delta x \ge \frac{6.626 	imes 10^{-34}}{0.45216} \approx 1.46 	imes 10^{-33} \ m$.

$A$ table-tennis ball has a mass of $10 \ g$ and a speed of $90 \ m/s$. If the speed can be measured within an accuracy of $4\%$,what will be the uncertainty in speed and position?

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