S = x cos θ , with x = ( 2.0 ± 0.2 ) cm and θ = ( 53 ± 2 ) ∘ . Find the maximum absolute error in S in cm to one significant figure.

Δ S = ∣ cos θ ∣Δ x + ∣ x sin θ ∣Δ θ . Δ θ = 180 2 π rad . Δ S = 0.6018 ( 0.2 ) + 2 ( 0.7986 ) 180 2 π = 0.1761 … cm → 0.2 cm .

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PhysicsErrorMiscellaneousMedium2 minQB

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$S = x cos θ$ , with $x = (2.0 \pm 0.2) cm$ and $θ = (53 \pm 2)^{\circ}$ . Find the maximum absolute error in S in cm to one significant figure.

Answer:

0.20

Solution:

$Δ S = ∣ cos θ ∣Δ x + ∣ x sin θ ∣Δ θ$ .

$Δ θ = \frac{2 π}{180} rad$ .

$Δ S = 0.6018 (0.2) + 2 (0.7986) \frac{2 π}{180} = 0.1761 \dots cm \to 0.2 cm$ .

Stream:JEESubject:PhysicsTopic:ErrorSubtopic:Miscellaneous

⏱ 2mℹ️ Source: QB

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