MCQ
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 : $\left. h =6.63 \times 10^{-34} \,Js \right]$
  • A
    $10$
  • $1$
  • C
    $3$
  • D
    $2$

Answer

Correct option: B.
$1$
b
$\Delta v =90 \times \frac{5}{100}$

$=4.5 \,m / s$

$\Delta$ v. $\Delta x=\frac{h}{4 \pi m }$

$\Delta x=\frac{h}{4 \pi m \cdot \Delta v}$

$=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 0.01 \times 4.5}$

$=1.17 \times 10^{-33}$

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