A metre rule is supported horizontally by two pivots as shown. The vertical displacement y at the centre of the rule is given by the equation

Question 25

A metre rule is supported horizontally by two pivots as shown.

The vertical displacement y at the centre of the rule is given by the equation

y = kML³ / wt³

where

k is a constant,

L is the distance between the pivots,

M is the mass of the rule,

t is the thickness of the rule and

w is the width of the rule.

In an experiment, the following results are obtained:

L = (80.0 ± 0.2) cm

M = (60 ± 1) g

t = (6.0 ± 0.1) mm

w = (23.0 ± 0.5) mm.

Which measurement contributes most to the uncertainty in the calculated value of y ?

A L                   B M                 C t                   D w

Reference: Past Exam Paper – June 2016 Paper 13 Q4

Solution:

Answer: C.

Displacement y = kML³ / wt³

k is a constant and so, does not contribute to the uncertainty in y.

y = kML³ / wt³

Δy/y = ΔM/M + 3(ΔL/L) + Δw/w + 3(Δt/t)

In terms of percentage uncertainties,

%y = %M + 3%L + %w + 3%t

Uncertainty due to mass M: 1/60 × 100 % = 1.67 %

Uncertainty due to distance L: 3 × (0.2/80 × 100) % = 0.75 %

Uncertainty due to width w: 0.5/23 × 100 % = 2.17 %

Uncertainty due to thickness t: 3 × (0.1/6 × 100) % = 5 %