A ball weighing 10 g is moving with a velocity of 90 m 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]

We use the Heisenberg uncertainty principle: $$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$, which gives $$\Delta x = \frac{h}{4\pi \cdot m \cdot \Delta v}$$.

The mass of the ball is $$m = 10$$ g $$= 0.01$$ kg. The velocity is 90 m/s and the uncertainty in velocity is 5%, so $$\Delta v = 0.05 \times 90 = 4.5$$ m/s.

Substituting the values: $$\Delta x = \frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 0.01 \times 4.5}$$.

Computing the denominator: $$4 \times 3.14 \times 0.01 \times 4.5 = 4 \times 3.14 \times 0.045 = 4 \times 0.1413 = 0.5652$$.

Therefore $$\Delta x = \frac{6.63 \times 10^{-34}}{0.5652} = 11.73 \times 10^{-34} = 1.173 \times 10^{-33}$$ m.

Rounded off to the nearest integer, the uncertainty in position is $$1 \times 10^{-33}$$ m, so the answer is $$1$$.