Physical Quantity

Imagine trying to build a house without a tape measure or cook without measuring ingredients. Measurement is essential in our daily lives. Similarly, physicists need precise measurements to understand the physical world. In this chapter of physics and measurement, we will explore the fundamentals of physics and measurement, focusing on length, mass, and time. We'll discuss accuracy, precision, and the use of various instruments in scientific experiments and everyday life.

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This Story also Contains

1. Physical Quantity
2. Types of Physical Quantity
3. Solved Example Based on Physical Quantity
4. Summary

In this article, we will cover the concept of Physical quantity. This concept falls under the broader category of Physics and Measurement which is a crucial chapter in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more. No direct question was asked about this concept In JEE and NEET but indirectly this concept is very important to learn the chapter on physics and measurement.

Physical Quantity

A quantity that can be measured and expressed in the form of laws is called a Physical quantity. A physical quantity is expressed completely by its magnitude and unit.

One physical quantity can be represented in terms of one or more units.

Amount of physical quantity (Q)=nu
n= numerical value or magnitude
u=unit

For a given amount of physical quantity

nu = constant

So, n1u1=n2u2= constant So, nα1u

So larger the unit smaller the magnitude.

Now let's understand the types of physical quantity

Types of Physical Quantity

There are mainly four main types of physical quantity which are mentioned below:

1) Scalar Quantity

The quantities having magnitude only are known as scalar quantities. It does not specify the direction.

Scalar quantity can be added or subtracted by the laws of addition or subtraction.

Examples-Distance, time, work, energy, etc

2) Vector Quantity

The quantities having both directions as well as magnitude are known as vector quantities. It has a specific direction.

Vector quantity can be added and subtracted according to vector laws of addition.

Examples - Displacement, force, velocity, acceleration, momentum, etc.

3) Tensor Quantity

Scalar and vector are special cases of a tensor. Tensors are represented in the multi-dimensional array, i.e., in different directions, tensors will have different magnitudes.

• If a tensor has only magnitude and no direction, it is called a scalar (a tensor of rank zero).
• If a tensor has magnitude and one direction, it is called a vector (a tensor of rank one).

Examples are stress, The moment of inertia, coefficient of viscosity.

4) Ratio Quantity

When a physical quantity is the ratio of two similar quantities.

eg. Relative density = density of object density of water at 4∘C

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Solved Example Based on Physical Quantity

Example 1: A metallic sphere floats in an immiscible mixture of water (density 103 kg/m3) and a liquid (density 8×103 kg/m3 ) such that its 23 part is in water and 13 part in the liquid. The density of metal is-

1) 50003 kg/m3 2) 100003 kg/m3 3) 5000 kg/m3 4) 2000 kg/m3

Solution:

weight of sphere = upthrust from water + upthrust from liquid

v =(23v×103×g)+(v3×8×103×g) or ρ=100003 kg/m3

Hence, the answer is option (2).

Example 2: What is true for the ratio of physical quantity-

1) It is the ratio of two similar quantity

2) It has no unit

3) An example is the relative density

4) All of the above

Solution:

Ratio Quantity -

When a physical quantity is the ratio of two similar quantities

- wherein

eg. Relative density = density of object density of water at 4∘C

Ratio is a physical quantity which is the ratio of two similar quantities. It is unit-less

Hence, the answer is the option 4.

Example 3: Statement 1: A tensor quantity not completely specified even by magnitude and direction.

Statement 2: stress and moment of inertia are tensor quantities

which of the above statements is/are true?

1) only 1

2) only 2

3) both

4) none

Solution:

Tensor Quantity - Which are not completely specified even by magnitude and direction.

example: moment of inertia, co-efficient of viscosity

Hence, the correct option is 3.

Example 4: For a physical quantity which of the following relation is true? [n- numerical value, u - unit ]

1) nαu2
2) nαu
3) n∝u
4) n∝1u

Solution:

For any physical quantity

Q = n u =constant

So, n α1/u

Hence, the answer is the option (4).

Example 5: Which one of these groups shows the scalar physical quantity-

1) Displacement, speed, work

2) Current, force, work

3) (correct)mass, charge, volume, electric potential

4) Charge, electric field, speed, work

Solution:

Scalar Quantity can be added or subtracted by the laws of addition or subtraction. It does not specify the direction.

Ex- displacement, force and electric field are vector quantities.

Hence, the correct option is 3.

Summary

In short, all of physics is based on measurement. Basic physical quantities, like length, mass, and time, are quantified in standard units, meters, kilograms, and seconds. Accuracy is a relative measure of diversity or error relative to the true value of the measure and precision is a measure of variation of the repeated measurements. To take these measurements, we will need some tools like rulers, balances, and clocks. Measurements serve in physics to provide the basis for laws, check hypotheses, and serve as the ground for technological discoveries. The principles of measurement are applicable even in day-to-day activities through scientific research for reproduction and reliability of results.