Question

A ball weighing $10g$ is moving with a velocity of $90m{s}^{-1}$. If the uncertainty in its velocity is 5%, then the uncertainty in its position is______$\times {10}^{-33}m$. (Rounded off to the nearest integer)
[Given: $h=6.63\times {10}^{-34}Js$]

Answer 1

m = 10 g = ${10}^{-2}$ kg

v = 90 m/s

$\Delta v=v\times$5%$=90\times 5/100=4.5m/s$
$m.\Delta v.\Delta x\ge \frac{h}{4\pi }$
${10}^{-2}\times 4.5\times \Delta x\ge \frac{6.63\times {10}^{-34}}{4\times \frac{22}{7}}$
$\Delta x\ge \frac{6.63\times 7\times 2\times {10}^{-34}}{9\times 4\times 22\times {10}^{-2}}$
$\Delta x\ge 1.17\times {10}^{-33}=x\times {10}^{-33}$

$x=1.17\approx 1$