A ball weighing 10 g is moving with a velocity of 90 ms -1. If the uncertainty in its velocity is 5 %, then the uncertainty in its position is × 10-33 m. (Rounded off to the nearest integer) [Given: . h =6.63 × 10-34 Js ]

Question

A ball weighing 10 g is moving with a velocity of 90 ms -1. If the uncertainty in its velocity is 5 %, then the uncertainty in its position is × 10-33 m. (Rounded off to the nearest integer) [Given: . h =6.63 × 10-34 Js ] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Δ v =90 × (5/100) =4.5 m / s Δ v . Δ x =( h /4 π m ) Δ x =( h /4 π m ⋅ Δ v ) =(6.63 × 10-34/4 × 3.14 × 0.01 × 4.5) =1.17 × 10-33

Q. A ball weighing $10 g$ is moving with a velocity of $90 m s^{- 1}$ . If the uncertainty in its velocity is $5%$ , then the uncertainty in its position is $\times 1 0^{- 33} m$ . (Rounded off to the nearest integer)
[Given : $h = 6.63 \times 1 0^{- 34} J s]$

$Δ v = 90 \times \frac{5}{100}$

$= 4.5 m / s$

$Δ v .Δ x = \frac{h}{4 πm}$

$Δ x = \frac{h}{4 πm \cdot Δ v}$

$= \frac{6.63 \times 1 0 ^{- 34}}{4 \times 3.14 \times 0.01 \times 4.5}$

$= 1.17 \times 1 0^{- 33}$

Q. A ball weighing 10g is moving with a velocity of 90ms−1. If the uncertainty in its velocity is 5%, then the uncertainty in its position is ×10−33m. (Rounded off to the nearest integer) [Given : h=6.63×10−34Js]

Δv=90×1005​ =4.5m/s Δv.Δx=4πmh​ Δx=4πm⋅Δvh​ =4×3.14×0.01×4.56.63×10−34​ =1.17×10−33

Q. A ball weighing $10 g$ is moving with a velocity of $90 m s^{- 1}$ . If the uncertainty in its velocity is $5%$ , then the uncertainty in its position is $\times 1 0^{- 33} m$ . (Rounded off to the nearest integer)
[Given : $h = 6.63 \times 1 0^{- 34} J s]$

$Δ v = 90 \times \frac{5}{100}$

$= 4.5 m / s$

$Δ v .Δ x = \frac{h}{4 πm}$

$Δ x = \frac{h}{4 πm \cdot Δ v}$

$= \frac{6.63 \times 1 0 ^{- 34}}{4 \times 3.14 \times 0.01 \times 4.5}$

$= 1.17 \times 1 0^{- 33}$