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SUPPLEMENTARY QUESTIONS

CHAPTER 1: PHYSICAL QUANTITIES AND UNITS: Prefixes, Derived

Units, Homogeneity.

1. Simplify the following terms that have prefixes and / or multiples into

scientific notation.

a. 100 μN

b. 1 × 10-4 km.

c. 200 mV – 1.5 × 105 μV

d. 325 nm.

e. 1.25 × 103 GHz.

2. Obtain the SI base units of the following derived quantities.

a. area,

b. acceleration,

c. force,

d. momentum,

e. work,

f. power,

g. electric charge,

h. potential difference, and

i. electrical resistance.

3. Show that the following equations are homogeneous:

a. The distance, � travelled in time �by a body which starts from rest and

travels with a uniform acceleration � is given by � = �����

b. The frequency � of vibration of a pendulum of length is given by the

equation � = ����

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4. Many constants in equations in science have dimensions.

a. Determine the SI base units of the universal gravitation constant �,

which occurs in � = � ������ where � is the gravitational force between

two masses �� and �� whose centres are a distance � apart.

b. Determine the SI base units of the gas constant � occurring in the ideal

gas equation �� = ���, which relates the pressure �, volume �, and

thermodynamic temperature � of � mole of an ideal gas.

5. The speed � of sound in a gas depends on the density � and pressure � of

the gas. If this dependence is in the form of a power law, that is

� = ���� ,

where �, �and ! are constants (� a dimensionless one).

a. Determine the values of � and !, and,

b. Thereby rewrite the above equation in simpler form.

6. When a sphere moves through a liquid, it might be reasonable to expect the

frictional force � on the sphere to depend on

η the viscosity of the liquid

� the speed of the sphere

� the radius of the sphere,

� the density of the liquid

The SI base unit of viscosity, η is �"�#��#�.

Assuming that � = $%�� �&�' where $, �, !, (and ) are dimensionless

constants. Use your understanding of homogeneity to simplify the above

equation by expressing !, ( and ) in terms of �.