A golf ball of mass '$m$' has a speed of $50 \mathrm{~ms}^{-1}$, If the speed can be measured within…
A golf ball of mass '$m$' has a speed of $50 \mathrm{~ms}^{-1}$, If the speed can be measured within accuracy of $2 \%$, the uncertainty in the position is
$\frac{h}{4 \pi m}$
$\frac{h}{16 \pi m}$
$\frac{h}{4 \pi m} \times 10^3$
$\frac{h}{16 \pi m} \times 10^3$
Solution
The uncertainty in the speed is $2 \%$ i.e.
$50 \times \frac{2}{100}=1 \mathrm{~ms}^{-1}$
According to Heisenberg uncertainty principle,
$\begin{aligned}
& \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{~m} \Delta \mathrm{v}} \\
& \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{~m} \times 1 \mathrm{~ms}^{-1} \mathrm{~g}} \quad\left[1 \mathrm{~g}=10^{-3} \mathrm{~kg}\right] \\
& \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{~m} \times 10^{-3}} \\
& \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{~m}} \times 10^3 \quad\left[1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-2}\right]
\end{aligned}$