Question

A golf ball has a mass of $40g,$ and a speed of $45m/s$ 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., $15\times \frac{2}{100}=0.9m{s}^{-1}$

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

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

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.