A golf ball has a mass of 40 g, and a speed of 45 m/s. If the speed can be measured within accuracy of 2%, calculate the uncertainty in the position.

Question

A golf ball has a mass of 40 g, and a speed of 45 m/s. If the speed can be measured within accuracy of 2%, calculate the uncertainty in the position. (A) 1.46×10-33 m (B) 1.46×10-33 c m (C) 1.59×10-33m (D) 1.39×1033 Km

Tardigrade Admin · Accepted Answer

The uncertainty in the speed is 2%, i.e.,

45 \times \frac{2}{100} = 0.9 m s^{- 1} .

Using the equation

Δ x = \frac{h}{4 πm Δ υ}

= \frac{6.626 \times 1 0 ^{- 34} J s}{4 \times 3.14 \times 40 \times 1 0 ^{- 3} K g ( 0.9 m s ^{- 1} )} = 1.46 \times 1 0^{- 33} m

This is nearly

\sim 1 0^{18}

times smaller than the diameter of a typical atomic nucleus. As mentioned earlier for large particles, the uncertainty principle sets no meaningful limit to the precision of measurements.

Q. A golf ball has a mass of 40 g, and a speed of 45 m/s. If the speed can be measured within accuracy of 2%, calculate the uncertainty in the position.

$1.46 \times 1 0^{- 33} m$

$1.46 \times 1 0^{- 33} c m$

$1.59 \times 1 0^{- 33} m$

$1.39 \times 1 0^{33} K m$

Q. A golf ball has a mass of 40 g, and a speed of 45 m/s. If the speed can be measured within accuracy of 2%, calculate the uncertainty in the position.

1.46×10−33m

1.46×10−33cm

1.59×10−33m

1.39×1033Km

$1.46 \times 1 0^{- 33} m$

$1.46 \times 1 0^{- 33} c m$

$1.59 \times 1 0^{- 33} m$

$1.39 \times 1 0^{33} K m$