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Question: What will be the uncertainty in velocity of a bullet with a mass of 10 g whose position is known wit...

What will be the uncertainty in velocity of a bullet with a mass of 10 g whose position is known with ±0.01\pm 0.01 mm?

A

5.275×10−33ms−15.275 \times 10^{- 33}ms^{- 1}

B

5.275×10−25ms−15.275 \times 10^{- 25}ms^{- 1}

C

5.275×10−5ms−15.275 \times 10^{- 5}ms^{- 1}

D

5.275×10−28ms−15.275 \times 10^{- 28}ms^{- 1}

Answer

5.275×10−28ms−15.275 \times 10^{- 28}ms^{- 1}

Explanation

Solution

: Δx=±0.01mm=1×10−5m,m=10g=1×10−2kg\Delta x = \pm 0.01mm = 1 \times 10^{- 5}m,m = 10g = 1 \times 10^{- 2}kg

Δv=h4πm.Δx=6.626×10−34Js4×3.14×10−2kg×10−5m\Delta v = \frac{h}{4\pi m.\Delta x} = \frac{6.626 \times 10^{- 34}Js}{4 \times 3.14 \times 10^{- 2}kg \times 10^{- 5}m}

=5.275×10−28ms−1= 5.275 \times 10^{- 28}ms^{- 1}