Force

Scientific Study

Unit: 1

Book Icon Class 10: Science

Scientific Study, Variables in Scientific Research, Types of Variables, Unit, Types of Units, Analysis of Unit wise Equation

Scientific Study

A scientific study, also known as a scientific investigation or research study, refers to a systematic and organized process of gathering and analyzing information to answer a specific research question or hypothesis. It involves the application of scientific methods and principles to explore, understand, or investigate a particular topic or phenomenon.  

In a scientific study, researchers follow a structured approach to collect data, conduct experiments, make observations, and analyze findings to conclude. The study aims to generate new knowledge, deepen understanding, or provide evidence-based insights in a specific field of study. 

Variables

In research, variables are any characteristics that can take different values. An experiment usually has three kinds of variables. 

1. Dependent Variable: The variable that is dependent on other variables is called dependent variable. 

2. Independent Variable: The variable that is not dependent on other variables is called an independent variable. 

3. Controlled Variable: The variable that is controlled during the experiment is called a controlled variable. 

Let's consider a simple example of growing plants to demonstrate the concepts of dependent, independent, and controlled variables. “Suppose you want to investigate the effect of different amounts of water on the growth of plants.” 

Dependent Variable: Height of Plant 

Independent Variable: Amount of Water 

Controlled Variable: Amount of Sunlight, Humidity, Initial Height of Plant, etc. 

Things to be noted while working with variables. 

  1. An experiment should have only one independent variable. 
  2. An experiment should have only one dependent variable. 
  3. Other variables apart from the dependent and independent variables should be controlled. 
  4. In a mathematical equation, the dependent variable should be on the left-hand side and the independent variable on the right-hand side. 
  5. When plotting a graph, the dependent variable should be plotted on the y-axis and the independent variable on the x-axis. 

 

Unit

The known quantity which is used in measurement is called a unit. All the physical quantities have units. The units of physical quantities are of two types 

Fundamental Unit 

The units of fundamental quantities which are independent of each other are called fundamental units. In the SI system, there are seven types of fundamental units. 

SN Physical Quantity Name of Unit Symbol 
1 Length Meter M 
2 Mass Kilogram kg 
3 Time Second S 
4 Temperature Kelvin K 
5 Luminous Intensity Candela cd 
6 Electric Current Ampere A 
7 Amount of Substance Mole Mol 

 

Derived Unit 

The units of physical quantities formed by combining two or more fundamental units are called derived units. For example: the units of Force, Velocity, work, etc. are derived units. 

SN Physical Quantity Related Formulae Name of Unit Symbol Fundamental Units Involved 
1 Area 

A = l x b 

Square Meter m2 m x m 
2 Volume 

V = l x b x h 

Cubic Meter m3 m x m x m 
3 Density 

D = M/V 

Kilogram/cubic meter Kg/m3 Kg/(m x m x m) 
4 Force 

F = ma 

Newton N (Kg x m)/(s x s) 
5 Pressure 

P = F/A 

Pascal N/m2 Kg/(m x s x s) 
6 Work/Energy 

W = F X d 

Joule J (Kg x m x m)/(s x s) 
7 Velocity 

V = s/t 

Meter/Second m/s2 m/(s x s) 

 

Analysis of Unit-wise Equation

The analysis of unit-wise equations involves examining the units of measurement associated with different quantities in an equation to ensure consistency and accuracy. This analysis is crucial in scientific and mathematical calculations to verify that the units on both sides of an equation are compatible and represent the same physical quantity. 

Here are the key steps involved in the analysis of unit-wise equations: 

  1. Identify the variables: Determine the variables present in the equation and their corresponding units. 
  2. Assign units to variables: Assign appropriate units to each variable based on the physical quantity it represents. 
  3. Analyze each term: Break down the equation into individual terms and examine the units associated with each term. Ensure that the units on both sides of the equation are the same and compatible. 
  4. Check dimensional consistency: Verify that the dimensions (units) of each term on both sides of the equation match.

By analyzing equations unit-wise, you can identify any inconsistencies, errors, or mismatches in units that may lead to incorrect calculations or interpretations. It helps ensure that equations accurately represent the relationships between physical quantities and enable proper understanding and analysis of scientific phenomena.  

Example: Check the validity of the following equations. 

  1. \(v^2 = u^2 + 2as\)

  2. \(s = ut + \frac{1}{2} at\)

Solution:

\(\begin{aligned} & \text{Here, } \\ & or, v^2 = u^2 + 2as \\ & or, m^2s^{-2} = m^2s^{-2} + ms^{-2} \times m \\ & \therefore m^2s^{-2} = m^2s^{-2} + m^2s^{-2} \end{aligned}\)

 In the above equation, The units on both left-hand and right-hand are the same. Hence, this equation is valid.  

Similarly,

\( \begin{aligned} & Here, \\ & or, s = ut + \frac{1}{2} at \\ & or, m = ms^{-1} \times s + ms^{-2} \times s \\ & \therefore m = m + ms^{-1} \end{aligned} \)

 In the above equation, The units on both left-hand and right-hand are not the same. Hence, this equation is invalid. 

 

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