# Chapter 1 - Worked Solutions

### to selected Complex Reasoning questions from the OUP text Senior Physics - Knowledge, Processes and Reasoning by Walding, Rapkins and Rossiter

Question 36

3 x 108 m ¸ 0.305 = 9.84 x 108 feet

9.84 x 108 feet ¸ 5280 = 186 289.12 miles

186 289.12 miles x 8 = 1 490 313 furlongs

1 fortnight = 14 days

14 days = 14 x 24 x 60 x 60 seconds = 1 209 600 s

In 1 fortnight light travels 1 490 313 x 1 209 600 furlongs = 1.8 x 1012 furlongs/fortnight.

Question 37

length = 756.5 ± 0.5 mm = 756.5 ± 0.07%

mass = 8.5 ± 0.5 g = 8.5 ± 6%

mass/mm = 8.5/756.5 = 1.1236 x 10-12 ± (6 + 0.07)%

= 1.1236 x 10-12 ± 6.8 x 10-4

= 1.1 x 10-12 (2SF) ± 7 x 10-4 (1SF) g/mm

Question 38

time = distance ¸ speed = 10-15 ¸ 3 x108 = 3 x 10-24 s

In 1 second there are 1 ¸ (3 x 10-24) fermis = 3 x 1023 fermis in 1 second.

Question 39

\$36 000 per year = \$690 per week (2SF)

Question 40

Total number of bytes = 200 x 220 = 200 x 1048576 = 2097152 or 2.097152 x 108

Number of 8 byte words = 2.097152 x 108 / 8 = 2.6214400 x 107 words.
This is written as 3 x 107 to one significant figure.

NOTE: There is an error in the question. A 'word' is actually two bytes not eight. There are 8 bits to a byte.

Question 41

The metre was defined as a particular length in 1983 and the speed of light measured in reference to this. The speed of light is a measured quantity, not a defined one like the metre or the second.

Question 42
1. Christians want to commemorate Easter on the correct day (actually - the first Sunday after the first full moon after the vernal equinox). This Sunday has to be correct.
2. 10 days adrift so March 1 in Moscow would be March 11 in London;
3. After 407 years there is a drift of 169 minutes so after 423 years the drift would be 169 x 423/407 = 176 minutes (2 h 56 m).

Question 43

Volume of 1 drop = 1/20 mL = 0.05 cm2
Area of drop = pr2 = 3.14 x 72 = 153.9 cm2
Volume = A x ht; ht = V/A = 0.05/153.9 = 3.25 x 10-4 cm = 3.25 x 10-6 m (= 3.25 mm).

Question 44

No. molecules in glass = 250mL/18 x 6 x 1023 = 8.33 x 1024.
No. glasses in oxcean = (1.3 x 1018 x 1000)/0.250L = 5.2 x 1021
Answer: true - more in glass.

Question 45

Volume = 4/3 pr3 = 4/3 p (20 x 103 x 102)3 = 3.35 x 1019 cm3.
D = m/V = (2 x 1030 )/(3.35 x 1019 )= 5.97 x 1010 kg/cm3.