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  1. Problems
  2. /Mechanics
  3. /Units and Measurement

Units and Measurement

Physics
+ Upload a Problem
More in MechanicsUnits and MeasurementMotion in a Straight LineRelative MotionVectors and Motion in a PlaneNewton's Laws of MotionFrictionWork, Energy and PowerMomentum and CollisionsCircular MotionGravitationRotational MotionElasticity and Mechanical Properties of SolidsPressure and FluidsFluid Flow, Bernoulli's Principle and ViscositySurface Tension and Capillarity
38 problems
Type:
1.
A student says: "I can find s = ut + 1/2at² by dimensions alone." Explain why not, and give two…
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
2.
In SI units G = 6.67 × 10⁻¹¹ N m² kg⁻², with dimensions [M⁻¹ L³ T⁻²].
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
3.
The speed v of a wave on a stretched string depends on the tension F and the mass per metre µ.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Hard
4.
The period T of a pendulum might depend on the bob's mass m, the length l and g.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Hard
5.
A swing dies down as x = A e⁻ᵇᵗcos(ω t), where t is time.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Hard
6.
The range of a projectile is R = (u² sin 2θ)/g.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
7.
A student cannot remember whether the energy stored in a stretched spring is 1/2kx or 1/2kx², where…
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
8.
Use dimensions to check v = u + at. The distance a body covers in its nth second is written sn = u…
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Easy
9.
Which of these have no dimensions? Relative density, coefficient of friction, efficiency of a…
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Easy
10.
Which of these pairs have the same dimensions?
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
11.
Use dimensions to check that GM/R² is an acceleration.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
12.
Find the dimensions of (a) density, (b) impulse (force times time), (c) surface tension (force per…
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Easy
13.
Round (a) 0.002 864 3 to three significant figures, (b) 456 780 to three significant figures, in…
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Easy
14.
Work out each one and write the answer properly: 3.6 × 2.15; 15.32 + 0.7 + 8.115; 9.00/1.5
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
15.
How many significant figures does each number have? 7.30; 0.0610; 5.008; 2.40 × 10⁵; 0.0007; 300.0
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Easy
16.
A student measures a pendulum's length as l = (0.800 ± 0.002) m, and times 30 swings as (53.7 ±…
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Hard
17.
A metal sphere has a mass of (40.0 ± 0.4) g and a diameter of (2.20 ± 0.01) cm.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Hard
18.
A rectangular metal plate measures (14.5 ± 0.1) cm by (6.0 ± 0.1) cm. Find its area with its error.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
19.
Two lengths are (15.6 ± 0.2) cm and (9.1 ± 0.1) cm.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Easy
20.
A screw gauge has a pitch of 1 mm and 100 circular divisions.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
21.
A vernier callipers has a least count of 0.01 cm (10 vernier divisions).
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
22.
A vernier callipers has a main scale marked every 0.5 mm.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Easy
23.
A student finds the acceleration due to gravity with a pendulum and gets 9.65 m/s².
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
24.
Five readings of the length of a pencil are 17.6 cm, 17.4 cm, 17.7 cm, 17.5 cm and 17.3 cm.
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Medium
25.
Say whether each error is systematic or random: a measuring tape that has stretched with use; gusts…
High School (11–12) · Units and MeasurementStemPy LabStemPy Lab
Easy
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