A ball weighing 10 g is moving with a velocity of 90 ms^$-$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]

m = 10 g = 10^$-$2 Kg<br><br>v = 90 m/sec.<br><br>$\Delta$ = v $\times$ 5% = 90 $\times$ ${5 \over {100}}$ = 4.5 m/sec<br><br>m . $\Delta$v . $\Delta$x $\ge$ ${h \over {4\pi }}$<br><br>10^$-$2 $\times$ 4.5 $\times$ $\Delta$x $\ge$ ${{6.63 \times 3 \times {{10}^{ - 34}}} \over {4 \times {{22} \over 7}}}$<br><br>$\Delta$x $\ge$ $${{6.63 \times 7 \times 2 \times {{10}^{ - 34}}} \over {9 \times 4 \times 22 \times {{10}^{ - 2}}}}$$<br><br>$\Delta$x $\ge$ 1.17 $\times$ 10^$-$33 = x $\times$ 10^$-$33<br><br>x = 1.17 $\simeq$ 1