A ball has a mass of 90 g and speed of 45 m/s. If speed can be measured with accuracy of 2%, then calculate uncertainty in position.
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A ball has a mass of 90 g and speed of 45 m/s. If speed can be measured with accuracy of 2%, then calculate uncertainty in position.
Please tell how to do this question. I have an exam tomorrow, so please don’t scam…
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Explanation:
ye 90 g hai ya 40 g maina apko 40g ke hisab sab sa kar ka dhika rahi hu koi baat nhi ap issa 40 g ka waja 90 g laga da na
Q A ball has a mass of 40 g and speed of 45 m/s. If speed can be measured with accuracy of 2%, then calculate uncertainty in position.
solution
Use Heisenberg's uncertainty principle.
For example [Δx=4πmΔvh]
Here, Δx is the uncertainty in the position.
Δv is the uncertainty in velocity
m is the mass of Particle.
Given,m=40g=0.04kg
Δv=2%ofv=2×10045=0.9m/s
h=6.626×10−34J.s
Now,Δx=(4×3.14×0.04×0.9)6.626×10−34
=1.4654×10−33m. Ans
With Another Method
Solution
Using heisenberg's uncertainty principle,
Δ=h/4πmΔv
Δx = uncertainty in position
Δv=2%ofv=2×45/100=0.9 m/s
now Δx=(4×3.14×0.04×0.9)6.626×10−34
=1.46×10−33 m. Ans
Verified answer
Explanation:
Using Heisenberg uncertainty principle
[tex]px \geqslant \frac{h}{4\pi} [/tex]
Where 'p' is uncertainty in momentum and 'x' is uncertainty in position.
Using the definition of momentum,
[tex]p = mv[/tex]
Where v is uncertainty in speed.
So using the equality we have,
[tex]mvx = \frac{h}{4\pi} [/tex]
[tex]x = \frac{h}{4\pi \times mv} [/tex]
Now , 2% accuracy in speed means
[tex]v = 0.02 \times 45 = 0.9 \\ mv = 81 \times {10}^{ - 3} [/tex]
Here we used mass in kg
so,
[tex]x = \frac{h}{4\pi \times 81 \times {10}^{ - 3} } [/tex]
This is the uncertainty in position with 'h' as the planck's constant
[tex]h = 6.63 \times {10}^{ - 34} [/tex]