An experiment to determine atmospheric pressure P uses the equation P = ρ gh where

Question 22

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

Reference: Past Exam Paper – November 2016 Paper 12 Q6

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.