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Question

A golf ball has a mass of 40g and a speed of 45 ms1. If the speed can be measured with an accuracy of 2%, calculate the uncertainty in the position.


A

1.46 × 1033 m

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B

2.62 × 1034 m

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C

7.84 × 1035 m

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D

5.55 × 1033 m

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Solution

The correct option is A

1.46 × 1033 m


By Heisenberg uncertainty principle,

p × x h4π v × x h4πm

Now,

Mass of the ball = 40 g = 40 × 103 kg

The uncertainty in the speed

v = 45 × 2100 = 0.9 m s1

So the uncertainty in postion,

x = h4πp = h4πmv

= 6.626×10344×3.14×(40×103kg)×(0.9ms1)

= 1.46 × 1033 m


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