Exam practice
Every question from the end of every unit, with hints and answers to open. After you check an answer, mark how you did, and come back to the ones you didn’t get.
17 questions
Unit 1 · Scientific Learning
2. Give reasons
The joule is a derived unit of work.
Answer
Work = force × distance, so its unit is N × m = kg m² s⁻². The joule is made by combining three fundamental units (kilogram, meter and second), and it can’t exist without them. A unit made from other units is a derived unit.
Some variables should be controlled while doing an experiment.
Answer
If anything besides the independent variable changes, it may also change the result, and then we can’t say what caused the effect. Keeping the other variables the same makes the test fair, so the result is valid and reliable.
is not a valid relation.
Answer
Left side: has units (m s⁻¹)² = m² s⁻². Right side: has units m s⁻¹ × s = m. The two sides have different units, so the equation can’t be correct.
3. Differentiate between
Independent variable and dependent variable
Answer
| Independent variable | Dependent variable |
|---|---|
| The experimenter changes it freely. | Its value depends on the independent variable. |
| It is the cause. | It is the effect. |
| Plotted on the x-axis; written on the right of an equation. | Plotted on the y-axis; written on the left of an equation. |
| e.g. the stretch of a rubber band | e.g. the distance the bullet flies |
Fundamental unit and derived unit
Answer
| Fundamental unit | Derived unit |
|---|---|
| Does not depend on any other unit. | Is made by combining fundamental units. |
| Can’t be broken into simpler units. | Can be broken into fundamental units. |
| There are only seven in SI. | There are many. |
| e.g. kilogram, meter, second | e.g. newton, joule, m/s |
4. Answer these questions
What is a unit?
Answer
A unit is a fixed, agreed amount of a physical quantity that other amounts are compared with when they are measured. For example, saying a rope is 5 m long means it is 5 times as long as one meter.
Write the SI units of mass, temperature, energy and density.
Answer
Mass: kilogram (kg). Temperature: kelvin (K). Energy: joule (J). Density: kilogram per cubic meter (kg/m³).
How is the validity of an equation checked? Give an example.
Answer
Write the units of every quantity in the equation in fundamental units and simplify. If both sides (and every term that is added or subtracted) have the same units, the equation may be valid; if not, it is certainly wrong.
Example: . Left: m s⁻¹. Right: is m s⁻¹, and is m s⁻² × s = m s⁻¹. All terms match, so the equation is valid.
Which fundamental units make up the unit of pressure?
Answer
Pressure = force ÷ area = (kg m s⁻²) ÷ m² = kg m⁻¹ s⁻². So the kilogram, meter and second.
Find the fundamental units in:
- i.newton (N)
- ii.watt (W)
- iii.joule (J)
- iv.pascal (Pa)
Answer
- i.N = kg m s⁻² (from F = ma)
- ii.W = J ÷ s = kg m² s⁻³ (from power = work ÷ time)
- iii.J = N × m = kg m² s⁻² (from work = force × distance)
- iv.Pa = N ÷ m² = kg m⁻¹ s⁻² (from pressure = force ÷ area)
Niva claimed that another formula for power is , and that a formula for pressure is . Check both by their units.
Hint
Work out the units of the right-hand side and compare them with the watt (kg m² s⁻³) and the pascal (kg m⁻¹ s⁻²).
Answer
Power: has units kg × (m s⁻¹)² = kg m² s⁻². The watt is kg m² s⁻³. They don’t match (kg m² s⁻² is the joule, a unit of energy), so this formula for power is invalid.
Pressure: has units kg × m s⁻¹ ÷ m² = kg m⁻¹ s⁻¹. The pascal is kg m⁻¹ s⁻². They don’t match, so this formula is invalid too.
Describe the independent, dependent and controlled variables, with an example of each.
Answer
- The independent variable is the one the experimenter changes on purpose (the cause).
- The dependent variable is the one that is measured, because it changes in response (the effect).
- Controlled variables are everything else that could affect the result; they are kept the same.
Example: testing how the amount of water affects the growth of bean plants. Independent: the amount of water per day. Dependent: the height of the plants after two weeks. Controlled: the type of seed, the soil, the size of pot, the sunlight and the temperature.
Karma connected a dry cell to a bulb with a few pieces of wire, and the bulb lit. He wondered how the thickness of the wire affects how long the dry cell lasts. Name the independent, dependent and controlled variables.
Answer
Independent: the thickness of the wire.
Dependent: the life of the dry cell (the time until the bulb goes out).
Controlled: the same kind of new dry cell each time, the same bulb, the same length of wire, the same metal in the wire, and the same room temperature.
Chandani wanted to find out how substances mixed into soil affect plant growth. She sieved a bucket of soil from a field and shared it equally among 12 pots of the same size. She mixed two spoons of lime into each of three pots, two spoons of urea into the next three, two spoons of table salt into the next three, and two spoons of compost into the last three. She planted similar seeds of the same plant in every pot, kept them all in a sunny place in the house, and watered all of them every day. Once the plants grew, she measured the height of each one daily.
- i.Name the independent, dependent and controlled variables in Chandani’s experiment.
- ii.Why did she use 3 pots for each substance?
Answer
- i.Independent: the substance mixed into the soil. Dependent: the height of the plants. Controlled: the same soil, the same size of pot, the same kind of seed, the same amount of substance (two spoons), the same sunlight and the same watering.
- ii.One plant can grow badly for a reason that has nothing to do with the substance: a weak seed, for example. With three pots for each, she can take the average height, and the result is more reliable.
Something to add: her experiment has no pots of plain soil with nothing mixed in. Without them she can compare the four substances with each other, but can’t say whether any of them helps the plant more than doing nothing. A group left unchanged for comparison is called a control group.
Subodh wanted to find out how the color of an object affects how much heat it holds. He painted four conical flasks with enamel: black, white, green and red. He filled them with water, closed each one tightly with a cork, and kept them in the sun. After some time he measured the temperature of the water in each flask with a thermometer. Name the independent and dependent variables. Which variables should Subodh control?
Answer
Independent: the color of the flask. Dependent: the temperature of the water.
To control: the same size and kind of flask, the same amount of water, the same starting temperature of the water, the same thickness of paint, the same place and time in the sun, the same time before measuring, and the same thermometer.
Manisha wanted to test her dog’s eating habits. She decided to study how the amount of food and the time of giving food affect how fast the dog eats. What is wrong with her experiment, and how can she fix it?
Answer
She is changing two independent variables at once. If the dog eats faster, she won’t know whether it was the amount of food or the time of day. She should test them one at a time: first change only the amount of food, giving it at the same time every day; then, in a separate test, change only the time, with the same amount of food each day.
Show that the unit of electrical resistance, the ohm (Ω), is kg m² s⁻³ A⁻².
Hint
Use , and potential difference = work ÷ charge, with charge (unit A s).
Answer
Charge: , so its unit is A s.
Potential difference: , so its unit is J ÷ (A s) = kg m² s⁻² ÷ (A s) = kg m² s⁻³ A⁻¹.
Resistance: , so its unit is kg m² s⁻³ A⁻¹ ÷ A = kg m² s⁻³ A⁻². That is the ohm.