H1.01. 2022 Measurement Answers to Examples, Quizzes _ Mini-tests

Measurement H1 Physics 1 Answers to Examples, Quizzes & Mini-test [Measurement] Quiz Spot the odd one out: Answer: kilogram is a unit, while the others are physical quantities. Example 6 Estimate the mass of a single sheet of A4 paper. A 0.01 g B 0.3 g C 1 g D 30 g Solution: 1. Estimate the mass of 1 ream of A4 size papers - 1 ream ‘feels’ heavier than a 1 litre bottle of water (1 kg) and lighter than a 5 kg bag of rice - Estimated mass of 1 ream = 3 kg 2. 1 ream of A4 size paper has 500 sheets 3. Mass of 1 A4 size paper = 3×1000 500 g = 6 g (100 - Order of magnitude) Answer: C MINI-TEST 1 1. What are the SI base units of k so that the following equation is homogeneous? velocity = k x density 2. Convert 1.3 g cm-3 to SI base units. 3. Which is a reasonable estimate for the volume of a metre rule found in a school laboratory? A 1.5 cm3 B 15 cm3 C 150 cm3 D 1500 cm3 My solution: 1. 2. kilogram length mass temperature time

Measurement H1 Physics 2 3. MINI-TEST 2 1. The acceleration of free fall g was to be determined by measuring the period of oscillation T and the length l of a simple pendulum, and using the formula g = 4π2l T2 In the experiment, the uncertainties in measuring l and T were estimated to be 4% and 1% respectively. If the value of g is experimentally found as 9.697 m s -2, determine the percentage uncertainty in g and express the value g with its uncertainty. 2. Errors in measurement may either be systematic or random. Which of the following involves random error? A Not allowing for zero error on a moving-coil voltmeter B Using an incorrectly calibrated balance to weigh objects C Stopping a stopwatch at the end of a race D Using the value of g as 10 N kg-1 when calculating weight from mass 3. For the vectors shown in Fig. 3.1 and Fig. 3.2, draw the vector diagram for (a) + AB (b) − AB

Measurement H1 Physics 3 4. Fig. 4.1 shows vectors C and D . (a) Use geometry and trigonometry to determine the magnitude and direction of =+ E C D . (b) Use vector resolution to determine the magnitude and direction of =+ E C D . My Solution: 1. 2. Fig. 4.1 3 m 4 m 60 20 y x Fig. 3.1 Fig. 3.2

Measurement H1 Physics 4 3. 4. (a) Using geometry and trigonometry Using cosine rule, = + −  E C D C D 2 2 2 2 cos ( )( )= + − = == oE E 2 224 3 2 4 3 cos100 29.168 29.168 5.40 m Using sine rule,  = osin sin100 3 5.40 ( ) −−  =  = =  o o11 sin100sin 3 sin 0.54712 33.25.40 E has a magnitude of 5.40 m and is in the direction of 26.8  (60 − 33.2) anti-clockwise above the x-axis. Fig. 3.1 Fig. 3.2 (a) (b) Fig. 3.1 (a) Fig. 3.2 (b) 3 m 4 m 30 20 70 

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