Question

A golf ball has a mass of $40\, g ,$ and a speed of $45 \,m / s$ If the speed can be measured within accuracy of $2 \%$ calculate the uncertainty in the position.

• A. $1.46 \times 10^{-33} m$
• B. $1.46 \times 10^{-33} cm$
• C. $1.59 \times 10^{-33} m$
• D. $1.39 \times 10^{33} km$

Answer 1

Answer: (A)

The uncertainty in the speed is $2 \%,$ i.e., $15 \times \frac{2}{100}=0.9\, m s ^{-1}$

Using the equation, $\Delta x=\frac{h}{4 \pi m \Delta v}$

$=\frac{6.626 \times 10^{-34} J s }{4 \times 3.14 \times 40 \times 10^{-3} kg \times 0.9 m s ^{-1}}=1.46 \times 10^{-33} m$

This is nearly $\sim 10^{18}$ times smaller than the diameter of a typical atomic nucleus. For large particles, the uncertainty principle sets no meaningful limit to the precision of measurements.