A Level Physics

Question 1

What does the SI unit refer to?

SI (International System of Units) is founded upon seven base units, including meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity.

The base units each have a unique definition agreed at world conventions.

Question 2

a.
i. Explain what is meant by a base unit.

ii. Give four examples of base units.

b. State what is meant by a derived unit.

a.
i. Base unit is one of a set of fundamental units in a system of measurement.

ii. Ampere, meter, second, kilogram.

b. Derived units consist of some combination of the base units. The base units may be multiplied together or divided by one another, but never added or subtracted. For instance, the unit of frequency is hertz (Hz) will have derived unit of `"s"^(-1)` or the moment of a force is measured in newton meter (`"N"."m"`) or `"kg"."m"^2."s"^(-2)`.

Question 3

What is the symbol for the SI base unit of temperature?

A. C

B. K

C. ^oC

D. ^oK

Answer: B

Kelvin doesn’t have degrees notation.

Question 4

Which list shows increasing lengths from beginning to end?

A. 1 cm - 1 nm - 1 mm - 1 `mu`m.

B. 1 `mu`m - 1 mm - 1 nm - 1 cm.

C. 1 nm - 1 `mu`m - 1 mm - 1 cm.

D. 1 mm - 1 cm - 1 `mu`m - 1 nm.

Answer: C
Each quantity has just one unit and this unit can have multiples and sub-multiples to cater for larger or smaller values. The unit is given a prefix to denote the multiple or sub-multiple.

Prefix	Symbol	Multiplying factor
tera	T	`10^12`
giga	G	`10^9`
mega	M	`10^6`
kilo	k	`10^3`
deci	d	`10^-1`
centi	c	`10^-2`
milli	m	`10^-3`
micro	μ	`10^-6`
nano	n	`10^-9`
pico	p	`10^-12`

Question 5

Which of the following is an SI base unit?

A. Ampere.

B. Coulomb.

C. Newton.

D. Joule.

Answer: A

It is noticed that SI is founded upon seven base units.

Question 6

Which of the following is not a SI base quantity?

A. Current.

B. Energy.

C. Mass.

D. Temperature.

Answer: B

It is noticed that SI is founded upon seven base units including meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity.

Question 7

Express the unit of following physical quantities in terms of SI base units:

a. Work done.

b. Moment of a force.

a. Work done is defined as the product of force and displacement. We know that The base unit of force is Newton, which can be expressed as: `"kg"."m"."s"^(-2)` and the base unit of displacement is meters, which is denoted as `"m"`.
Hence, the base unit of work done is `("kg"."m"."s"^(-2))."m"="kg"."m"^2."s"^(-2)`.

b. The moment of a force (torque) is defined as the product of the force and the distance from the pivot point:

`"moment of force" = "force" xx frac{"perpendicular distance"}{"lever arm"}`.

Same as work done, the base unit of the moment of a force is `"kg"."m"^2."s"^(-2)`.

Question 8

The drag force acting on a car moving with speed $v$ along a straight horizontal road is given by:
`"F"_D = "v"^2."A"."k"`, where is a constant and $A$ is the cross-sectional area of the car. Determine the SI base units of .

We are given: `"F"_"D" = "v"^2."A"."k"`

Rearrange: `"k" = "F"_"D" / ("v"^2 ."A")`

SI base unit of force: `"F" = "m"."a" => "Unit" = "kg"."m"."s"^-2`

SI base unit of velocity squared: `"v" = "m"."s"^-1 => "v"^2 = "m"^2."s"^-2`

SI base unit of area: `"A" = "m"^2`

Substituting all units into $("kg"."m"."s"^-2) / ("m"^2."m"^2."s"^-2)``"k" = "kg"."m"^-3`$

Question 9

The current $I$ in a metal wire is given by the expression: where:

is the average drift speed of the free electrons in the wire.

is the number of free electrons per unit volume (number density).

$A$ is the cross-sectional area of the wire.

$e$ is the elementary charge.

Use the expression to determine the SI base units of e.

We are given `"I" = "A" ."n"."v"."e" => "e" = "I" / ("A"."n"."v")`

Units of each quantity:

Current: I = A

Area: `"A" = "m"^2`

Number density: `"n" = "m"^-3`

Drift velocity: `"v" = "m"."s"^-1`

`"e" = "A" / ("m"^2."m"^-3."m"."s"^-1)`

`"e" = "A"."s"`

Question 10

a. Use an expression for work done, in terms of force, to show that the SI base units of energy are kg.m².s⁻².

b. The energy E stored in an electrical component is given by `"E"= "Q"^2/(2"C")`, where Q is charge and C is a constant.

Use this equation and the information in a.energy stored in an electrical component: to determine the SI base units of C.

a. Work done is defined as the product of force and displacement: `"Work" = "Force" xx "Displacement"`
From Newton's second law, force is defined as mass times acceleration:
`"Force" = "Mass" xx "Acceleration"`
Acceleration is the change in velocity per unit time: `"Acceleration" = "m"."s"^2`
So, the SI units of force are: `"Force" = "kg"."m"."s"^-2`
Substitute this into the formula for work: `"Work" = ("kg"."m"."s"^-2)."m" = "kg"."m"^2."s"^-2`
The SI base units of energy is: `"kg"."m"^2."s"^-2`

b. Energy stored in an electrical component: `"E" = "Q"^2 / (2"C") => "C" = "Q"^2 / (2"E")`

Electric charge is current times time: `Q=I×t⇒"unit of" " " Q=A.s`
`"Q"^2 = "A"^2 xx "s"^2`
From part a. unit of `"E" = "kg"."m"^2."s"^-2`

We have `"C" = "Q"^2 / (2"E")`

Substitute into C: `"C" = ("A"^2."s"^2) / (2."kg"."m"^2."s"^-2)`

`"C" = "kg"^-1."m"^-2."A"^2."s"^4`.