Question

Q51)
51. A ball of mass 50 g moves with a speed of 50 ms-?. If the speed is measured
within accuracy of 2%, the uncertainty in the position is
1) 1.06 x 10-34 m 2)1.06 x 10-33 m 3)6.626 x 10-34 m
4)6.626 x 10-33
O 1
m
O 2
3
o
4
052)​

Answer 1

Answer:

$1.06$ × $10^{-34} m$

Explanation:

Given: Mass (m) of the ball is 50g

speed of the ball is $50 m/s$

Accuracy = 2%

Step: 1

We know that $1 kg =1000 g$

By using this conversion we get Mass as $\frac{50}{1000}Kg =$ 50× $10^{-3}Kg$

Now, by calculating the speed we get:

ΔV = $50$×$\frac{2}{100} = 1.0 m/s$

Step 2:

Using uncertainty formula :

Δx . ΔP = $\frac{h}{4\pi }$

Where we know that ΔP is mΔv

Now, on further calculating we get:

Δx = h/4$\pi$×mΔv

Δx = 6.626 × $10^{-34} Js$ / 4× 3.14× 50 ×$10^{-3} kg$ × 1.0 m/s

Δx= 1.06 ×$10^{-34} m$

Hence, If the speed is measured within the accuracy of 2%, the uncertainty in the position is 1.06 ×$10^{-34} m$

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