Question

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

Doubt :- How come 2% of 45 m/s which is the accuracy in velocity be used as uncertainty in velocity in the given solution?
If it is wrong, please show the correct one and if the given solution is correct then
how come.

Answer 1

Here Accuracy means The change in Velocity/ Uncertainity in Velocity


Use Heisenberg's uncertainty principle,
e.g., ∆x = h/4πm∆v
Here, ∆x is the uncertainty in position
∆v is the uncertainty in velocity
m is the mass of Particle .

Given, m = 40g = 0.04kg
∆v = 2% of v = 2 × 45/100 = 0.9 m/s
h = 6.626 × 10⁻³⁴ J.s
Now, ∆x = 6.626 × 10⁻³⁴/(4 × 3.14 × 0.04 × 0.9)
= 14.654 × 10⁻³⁴ m

Hence, uncertainty in position = 1.4654 × 10⁻³³ m


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