Class 10 Scientific Learning Exercise 1.1 Solutions | Oasis School Science and Technology Oasis Publication Private Limited

Option A is correct option.

Given equation is a homogenous equation because all of its terms can be expressed in terms of the same unit (in this case, units of velocity squared, acceleration, and displacement).

It is not non-homogeneous, as that would indicate terms with differing units. The term analogous does not apply here, as it suggests a relationship to a different situation rather than describing motion under uniform acceleration. Lastly, while the equation contains variables, it is not simply a variable equation, it defines a specific relationship among those variables under constant conditions, rather than allowing them to change independently.

Option C is the correct answer.

The height of the plant is the dependent variable in the given experiment. This is because the observable impact of watering the plant every day can only be noticed in the height of the plant.

For this experiment, variables such as the amount of water, the quantity of soil, and the size of the water pot must be controlled. Otherwise, they may invite anomalies to the observations.

The independent variable is the act of turning the bulb on and off.

Reason: The independent variable is often the cause of the effect in the experiment. The scientist is researching the behaviour of an earthworm (effect) in response to the act of turning a bulb on and off (cause). Hence, the act of turning the bulb on and off is the independent variable.

It is a controlled variable if its magnitude is constant throughout the experiment.

Several factors may influence the results of an experiment. Therefore, we generally control the influence of factors other than the dependent and independent variables in the experiment. All those variables that remain constant throughout the experiment are called controlled variables.

The quantities that can be measured are called physical quantities. They maybe scalar or vector quantities. 

The standard reference quantity of a physical quantity is called a unit. Units provide a consistent way to measure and express physical quantities, allowing for clear communication and comparison of measurements. For example, common units include meters for length, kilograms for mass, and seconds for time.

Area is a derived quantity as it depends on power of a fundamental quantity i.e. length (meter).

Area(A) = length . breadth = \(\rm m^{2}\)

The physical quantity represented by \(\rm kgms^{-2}\) is force. This unit is known as a newton (N), which is the standard unit of force in the International System of Units (SI). One newton is defined as the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

Independent variable is changed by the scientist during the experiment.

These variables are the causative factors of any experiment. A researcher is free to manipulate the values of such variables.

Density is the physical quantity in the ratio of mass to volume. 

Density is defined as the mass of a substance per unit volume. It is a measure of how much mass is contained in a given volume and is typically expressed with the formula:

\(\rm Density\) = $\frac{Mass}{Volume}$

The SI unit of density is kilogram per cubic meter (\(\rm kgm^{-3}\)).

More than two variables (dependent and independent) can influence the results of an experiment. To increase an experiment's accuracy and reliability and eliminate any form of inconsistencies in the experiment, controlled variables are important.

Mass is a fundamental physical quantity. Its unit, kilogram (kg), is called a fundamental unit because:

• it does not depend upon any other physical quantity for its definition,
• it has its own identity,
• units of many other physical quantities depend upon kilogram for their definition. 

Hence, the unit of mass is called the fundamental unit.

Unit-wise analysis is used to test physical equations for several key reasons:

1. Dimensional Consistency: It ensures that both sides of an equation have the same dimensions (units). If they don't match, the equation is likely incorrect.
2. Error Detection: Analyzing units helps identify mistakes in calculations or formulations. Mismatched units signal potential errors.
3. Simplification and Insight: It simplifies complex equations and provides insight into the relationships between physical quantities, making it easier to understand how they interact.

Overall, unit-wise analysis is essential for ensuring accuracy and clarity in physics.

The differences between Fundamental units and Derived units are mentioned in the table below: