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 %
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