1. Scientific Study — Overview
Scientific study covers scientific facts, theories, models, experiments, and physical situations. It examines objects in nature in a planned, organized, and logical way, based on the scientific method and measurable evidence.
Variable: A causative factor, characteristic, or trait that has a direct or indirect relationship with an event or phenomenon.
Every incident or change has a cause and an effect. The cause is the causative factor, and the change it produces is the effect. To predict outcomes accurately, we must know the relationship between the size of the cause and the size of the effect. This relationship is found through experiments.
1.1 Variables of Scientific Research
When we observe a phenomenon, we naturally want to know why it happens and what factors are responsible. Investigating this helps us predict outcomes and take correct action (for example, understanding why a plant wilts helps us know how to save it).
Scientific research involves changing the value of one physical quantity and observing the resulting change in another physical quantity. Because their values change during the experiment, these physical quantities are called variables.
Variables of an experiment: the physical quantities that change or may change during that experiment.
Each variable is given a name and represented by a symbol. The relationship between variables is written as a mathematical formula (for example, if extension of a rubber band is 'e' and distance travelled by an object is 'x', then x ∝ e).
Types of Variables
Variables are usually classified into three types: independent variable, dependent variable, and controlled variable.
a) Independent Variable
The variable that the researcher deliberately changes or manipulates by a chosen amount during an experiment. It is the causative factor. The researcher is free to decide its value.
- It causes the change in the experiment.
- Example: In a catapult experiment, the extension of the rubber band is the independent variable.
- Other examples of independent variables: amount of fertilizer, sunlight, or water given to a plant.
b) Dependent Variable
The variable whose value depends on the value of the independent variable. The researcher cannot set or predict its value directly — it must be measured after the experiment.
- It is the effect produced by the independent variable.
- Example: The distance travelled by the paper bullet (depends on how much the rubber band is stretched).
- Example: The height/growth of a plant depends on the amount of sunlight given (independent variable).
c) Controlled Variable
When an experiment has more than one variable that could affect the result, it becomes difficult to know which variable actually caused the change, making the conclusion unreliable. So, all variables other than the specified independent and dependent variable must be kept constant (controlled) throughout the experiment.
- Controlled variables are kept the same in every trial so they do not affect the result.
- Example: Thickness of rubber band and size of paper bullet (kept constant in the catapult experiment).
- Example: Initial size of plants, and the amount of air, water and manure supplied (kept constant while studying the effect of sunlight on plant growth).
- Example: Concentration of acid and the quantity/weight of limestone (kept constant while studying the effect of surface area on reaction rate).
Examples of the Three Variable Types
| Subject of Research | Independent Variable | Dependent Variable | Controlled Variable |
|---|---|---|---|
| Rotating a tap knob and rate of water flow | Angle of rotation of knob | Amount of water flow per minute | Water pressure |
| Electricity and magnetism in a solenoid | Amount of electric current | Number of pins attracted by the electromagnet | Number of turns in solenoid, size of pin |
| Effect of heat on solubility of sugar | Temperature of water | Amount of sugar dissolved | Amount of water (always 100 g) |
| Effect of exercise on heartbeat | Duration of physical exercise | Number of heartbeats | Type of exercise, rest interval before counting |
Important Points about Variables
- 1There should be only one independent variable in an experiment.
- 2There should be only one dependent variable in an experiment.
- 3Except for the specified independent and dependent variable, all other variables should be controlled.
- 4In an equation, the dependent variable is usually written on the left side and the independent variable on the right side. Hence the independent variable is also called the right variable, and the dependent variable is called the left variable. (Example: s = vt — here s is dependent, t is independent, v is controlled.)
- 5On a graph, the dependent variable is always plotted on the vertical line (y-axis) and the independent variable on the horizontal line (x-axis). So the dependent variable is also called the y-variable (vertical variable), and the independent variable is called the x-variable (horizontal variable).
1.2 Types of Units
Physical quantities are measured in units. Units of all physical quantities are divided into two types: Fundamental unit and Derived unit.
Fundamental Unit
A unit of measurement that has independent existence, does not depend on any other unit, and cannot be broken down into simpler forms. There are 7 fundamental units in the SI system.
| Physical Quantity | Fundamental Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Luminous intensity | candela | cd |
| Electric current | ampere | A |
| Amount of substance | mole | mol |
Derived Unit
A unit of measurement that has no independent existence and is formed by combining two or more fundamental units. Some derived units are given a special short name; others use the combination directly.
- Density = kg/m³ (combination of kilogram and metre; no special name).
- Force: kg·m·s⁻² is given the special name newton (N). So N = kg·m·s⁻².
- Pressure: kg·m⁻¹·s⁻² is given the special name pascal (Pa).
Common Derived Units
| Quantity | Formula | Fundamental Units Involved | Derived Unit / Name |
|---|---|---|---|
| Area | l × b | m² | m² |
| Volume | l × b × h | m³ | m³ |
| Density | mass / volume | kg/m³ | kg/m³ |
| Velocity | displacement / time | m/s | m/s |
| Acceleration | velocity / time | m/s² | m/s² |
| Force | mass × acceleration | kg·m/s² | Newton (N) |
| Pressure | force / area | kg/(m·s²) | Pascal (Pa) |
| Work | force × distance | kg·m²/s² | Joule (J) |
| Power | work / time | kg·m²/s³ | Watt (W) |
| Moment | force × distance | kg·m²/s² | N·m |
| Frequency | 1 / time | s⁻¹ | Hertz (Hz) |
Difference: Fundamental Unit vs Derived Unit
| Fundamental Unit | Derived Unit |
|---|---|
| Does not depend on other units. | Depends on the fundamental units. |
| There are 7 fundamental units used till now. | Many derived units are formed from the 7 fundamental units. |
Worked Examples: Finding Composition of Derived Units
a) Unit of area (square metre)
Area = length × breadth = m × m = m². So the unit of area, m², is formed from one fundamental unit (metre) used twice.
b) Unit of force (Newton, N)
By definition, F = m × a. Unit of mass (m) = kg, unit of acceleration (a) = m·s⁻². So N = kg·m·s⁻². Kilogram, metre and second are the fundamental units combined to form the newton.
1.3 Analysis of Unit-wise Equations (Dimensional Analysis)
The validity of a scientific formula or equation can be checked by comparing the units on both sides. For an equation to be valid, the units on the left-hand side (LHS) and right-hand side (RHS) must be exactly the same.
Rule for Checking Validity
- Write the fundamental unit of the quantity on the LHS.
- Write the fundamental unit of the quantity on the RHS by substituting the units of each term.
- If LHS unit = RHS unit, the equation is valid; otherwise, it is invalid.
Example 1 (Valid Equation)
Equation: s = v × t
LHS unit = m. RHS unit = (m·s⁻¹) × s = m. Since LHS = RHS, this equation is valid.
Example 2 (Invalid Equation)
Equation: s = v / t
LHS unit = m. RHS unit = (m·s⁻¹) / s = m·s⁻². Since LHS ≠ RHS, this equation is not valid.
Example 3 (Checking v² = u² + 2as)
LHS unit: v² → m²s⁻².
RHS unit: u² → m²s⁻², and 2as → (m·s⁻²)(m) = m²s⁻².
Since every term has the unit m²s⁻², LHS = RHS, so the equation is valid.
Addition/Subtraction Rule
Two physical quantities can only be added or subtracted if they have the same fundamental unit composition.
- u + v is possible: both have unit m·s⁻¹.
- s − at² is possible: both s and at² simplify to unit m.
- s + at is NOT possible: s has unit m, but at has unit m·s⁻¹ — different units cannot be combined.
Key Terms to Remember
| Term | Meaning |
|---|---|
| Variable | A factor/quantity that can change in an experiment. |
| Independent variable | The variable changed/controlled by the researcher (the cause). |
| Dependent variable | The variable that is measured/observed; depends on the independent variable (the effect). |
| Controlled variable | A variable kept constant throughout the experiment so it does not affect the result. |
| Fundamental unit | A unit that is independent and cannot be broken into simpler units (7 in SI system). |
| Derived unit | A unit formed by combining two or more fundamental units. |
| Unit analysis | Checking whether an equation is valid by comparing the units on both sides. |
Quick Revision Summary
- A variable is a factor that can change and affect the outcome of an experiment.
- Independent variable = cause (changed by researcher); Dependent variable = effect (measured); Controlled variable = kept constant.
- Dependent variable → left side of equation / y-axis of graph. Independent variable → right side of equation / x-axis of graph.
- 7 fundamental units: metre, kilogram, second, kelvin, candela, ampere, mole.
- Derived units are combinations of fundamental units (e.g., N = kg·m·s⁻², Pa = kg·m⁻¹·s⁻², J = kg·m²·s⁻²).
- An equation is valid only if the units on both sides are equal (checked using unit/dimensional analysis).
- Quantities can be added/subtracted only if they have the same unit composition.