Q#22 (Past Exam Paper – November 2016 Paper 12 Q6)
An experiment to determine atmospheric pressure P uses the equation P = ρ gh where
ρ = (13 600 ± 100) kg m-3,
g = (9.81 ± 0.02) m s-2,
h = (0.762 ± 0.005) m.
What is the value of P, with its uncertainty, when stated to an appropriate number of significant figures?
A (1.0166 ± 0.0162)×105 Pa
B (1.017 ± 0.016)×105 Pa
C (1.017 ± 1.6%)×105 Pa
D (1.02 ± 0.02)×105 Pa
Solution:
Answer: D.
Pressure P = ρgh = 13600 × 9.81 × 0.762
Pressure P = 1.0166 Pa
ΔP / P = Δρ/ρ + Δg/g + Δh/h
ΔP = (Δρ/ρ + Δg/g + Δh/h) × P
ΔP = (100/13600 + 0.02/9.81 + 0.005/0.762) × 1.0166 = 0.016 Pa
Uncertainty should always be given to 1 significant figure (s.f.). So, 0.016 should be rounded to 0.02.
The number of decimal place (d.p.) for the actual value of pressure P should follow the same number of d.p. as in the uncertainty.
In this case, the uncertainty is given to 2 d.p. So, the actual value of P should also be given to 2 d.p.
Post a Comment for " An experiment to determine atmospheric pressure P uses the equation P = ρ gh where"