Question

Calculate the uncertainty in the velocity of a wagon of mass 4000kg
whose position is known accurately of ± 4 m

Answer 1

$\bull\sf Mass\:of\:wagon=m=4000kg$

$\bull\sf Uncertainity\:in\:position=\triangle x=4m$

$\bull\sf Uncertainty\: in\:velocity=\Delta v=?$

According to Heisenberg's Uncertainty Principle

$\boxed{\sf \Delta x.\Delta P\geqslant \dfrac{h}{4\pi}}$

$\\ \sf\longmapsto \Delta x\times m\Delta v\geqslant \dfrac{h}{4\pi}$

$\\ \sf\longmapsto \Delta v=\dfrac{h}{4\pi\times \Delta x\times m}$

$\\ \sf\longmapsto \Delta v=\dfrac{6.626\times 10^{-34}Js}{4\times 3.142\times 4\times 4000kg}$

$\\ \sf\longmapsto \Delta v=\dfrac{6.626\times 10^{-34}}{2.0\times 10^{5}}$

$\\ \sf\longmapsto \Delta v=3.313\times 10^{-29}m/s$