A golf ball of mass m has a speed of 50 m s | vedclass

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Question

(A) The uncertainty in the speed $\Delta v$ is $2 \%$ of $50 \ m \ s^{-1}$.$\Delta v = 50 	imes \frac{2}{100} = 1 \ m \ s^{-1}$.According to Heisenbe

Vedclass · Accepted Answer

$\frac{h}{4 \pi m}$

Vedclass · Answer

(A) The uncertainty in the speed $\Delta v$ is $2 \%$ of $50 \ m \ s^{-1}$.$\Delta v = 50 	imes \frac{2}{100} = 1 \ m \ s^{-1}$.According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta p \geq \frac{h}{4 \pi}$.Since $\Delta p = m \Delta v$,we have $\Delta x = \frac{h}{4 \pi m \Delta v}$.Substituting the value of $\Delta v = 1 \ m \ s^{-1}$:$\Delta x = \frac{h}{4 \pi m 	imes 1} = \frac{h}{4 \pi m}$.Wait,re-evaluating the calculation: The question implies the uncertainty in speed is $1 \ m \ s^{-1}$.$\Delta x = \frac{h}{4 \pi m (1)} = \frac{h}{4 \pi m}$.However,looking at the provided options,if the mass $m$ is in $kg$ and we consider standard units,the calculation leads to $\frac{h}{4 \pi m}$.Given the options,if the result is $\frac{h}{4 \pi m}$,option $A$ is correct.

$A$ golf ball of mass $m$ has a speed of $50 \ m \ s^{-1}$. If the speed can be measured within an accuracy of $2 \%$,the uncertainty in the position is

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