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Answer:
The minimum uncertainty in its position is 1.85 x 10⁻³² m.
Explanation:
Given;
mass of the ball, m = 47.5 g = 0.0475 kg
speed of the ball, v = 30 m/s
measuring accuracy of the speed, = 0.2% = 0.002
The uncertainty in measurement of momentum;
ΔP = mΔv
ΔP = (0.0475)(30 x 0.002)
ΔP = 2.85 x 10⁻³ kgm/s
The uncertainty in position is calculated as;
[tex]\delta x \geq \frac{h}{4\pi (\delta P)}[/tex]
where;
h is Planck's constant
[tex]\delta x \geq \frac{6.626 \ \times \ 10^{-34}}{4\pi (2.85 \ \times \ 10^{-3})} \\\\\delta x \geq 1.85 \ \times \ 10^{-32} \ m[/tex]
Thus, the minimum uncertainty in its position is 1.85 x 10⁻³² m.