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A golf ball has a mass of 40g , and a sp...

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

Text Solution

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The uncertainty in the speed is 2%, i.e.,
`45xx(2)/(100)=0.9ms^(-1)`
Using the `lamda=(h)/(mv)=(h)/(P)`
`Deltax=(h)/(4pimDeltav)`
`(6.626xx10^(-34)Js)/(4xx3.14xx40gxx10^(-3)kgg^(-1)(0.9ms^(-1)))`
`=1.46xx10^(-33)m`
This is nearly `~10^(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.
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