- Core Content
Diagnostic Quiz: 2026/2027 Specification
Section A: Mechanics and Materials
Q1:
A student measures the mass of a metal cube as 50.0±0.1g and the length of one side as
2.00±0.01cm . She calculates the density. What is the percentage uncertainty in her calculated
density?
A. 0.2%
B. 1.7% [CORRECT]
C. 1.8%
D. 3.2%
Rationale: The correct answer is B. For multiplication and division, percentage uncertainties add.
For a cube, volume V∝L
3
, so the percentage uncertainty in volume is 3×
2.00
0.01
, ×100%=1.5% . The percentage uncertainty in mass is
50.0
0.1
×100%=0.2% . Total percentage uncertainty in density ρ= m/V is 1.5%+0.2%=1.7% . Distractor
A is incorrect because it only considers the mass uncertainty. Distractor C incorrectly adds the
length uncertainty linearly (0.5%+0.2% ) rather than accounting for the power of 3. Distractor D
incorrectly triples the combined linear uncertainty (3×(0.5%+0.2%) ).
Q2:
A ball is thrown vertically upwards with an initial speed of 12m s
−1
. What is the time taken to reach a point 5.0m above the projection point on its way down?
(g =9.81m s
−2
)
A. 0.53s
B. 1.2s
C. 1.9s [CORRECT]
D. 2.4s