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Question:

A physical quantity X is given by X = 2k³l²m⁻¹n. The percentage error in the measurements of k, l, m, and n are 1%, 2%, 3%, and 4% respectively. Find the percentage error in X.

10

12

None of these

8

Solution:

Given : X = 2k³l²m⁻¹n
∴ ΔX/X = 3(Δk/k) + 2(Δl/l) + (Δm/m) + (1/2)(Δn/n)
Percentage error in X
ΔX/X × 100 = (3(Δk/k) + 2(Δl/l) + (Δm/m) + (Δn/n)) × 100
= (3 × 1% + 2 × 2% + 3% + 4%) = 3% + 4% + 3% + 4% = 14%
Therefore, the percentage error in X is 14%.