Verified Solution • 2025–26 Session moderate

QJEEM21Chd593: JEE Main 2021 Chemistry - Class 11 JEEM21Chd593 Solution: A ball weighing 10 g is moving with a velocity of 90 ms 1 . If…

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 ___________ ×\times 10 −- 33 m. (Rounded off to the nearest integer)

[Given : h = 6.63 ×\times 10 −- 34 Js]

Step-by-Step Verified Solution

m = 10 g = 10 −- 2 Kg

v = 90 m/sec.

Δ\Delta = v ×\times 5% = 90 ×\times 5100{5 \over {100}} = 4.5 m/sec

m . Δ\Delta v . Δ\Delta x ≥\ge h4π{h \over {4\pi }}

10 −- 2 ×\times 4.5 ×\times Δ\Delta x ≥\ge 6.63×3×10−344×227{{6.63 \times 3 \times {{10}^{ - 34}}} \over {4 \times {{22} \over 7}}}

Δ\Delta x ≥\ge 6.63×7×2×10−349×4×22×10−2{{6.63 \times 7 \times 2 \times {{10}^{ - 34}}} \over {9 \times 4 \times 22 \times {{10}^{ - 2}}}}

Δ\Delta x ≥\ge 1.17 ×\times 10 −- 33 = x ×\times 10 −- 33

x = 1.17 ≃\simeq 1

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