ISC Physics: Units and Dimension

Practice flashcards covering physical quantities, SI units, systems of measurement, dimensions, and practical units of mass, area, and angles.

What are Physical quantities and how can they be expressed mathematically?

Physical quantities are all those quantities which can be measured directly or indirectly and in terms of which the laws of Physics can be expressed; they are defined by the formula $P = nu = \text{Constant}$, where $n$ is the numerical value and $u$ is the unit, or $n_1 u_1 = n_2 u_2$.

Distinguish between Fundamental Quantity and Derieved Quantity as defined in the notes.

A Fundamental Quantity is treated as independent and is not defined in terms of other physical quantities, while a Derieved Quantity is one whose defining operations are based on other physical quantities.

Identify the 7 base units of the S.I. system and their symbols as provided in the lecture material.

Length: meter ($m$), Mass: Kilogram ($kg$), Time: Second ($s$), Amount of substance: mole ($mol$), Thermodynamic Temp.: Kelvin ($K$), Electric current: amperes ($A$), and Luminous intensity: Candela ($ed$).

Describe the three systems of units (F.P.S, C.G.S., and M.K.S) for measuring length, mass, and time.

F.P.S uses foot, Pound, and Second; C.G.S. uses Centimeter, Gram, and Second; M.K.S uses Meter, Kilogram, and Second.

What is the definition of the dimension of a physical quantity?

The powers (or exponents) to which the fundamental quantities must be raised to represent that quantity completely.

List the symbols used in a dimensional formula for Mass, Length, Time, Current, Temperature, and Amount of substance.

Mass: $(M)$, Length: $(L)$, Time: $(T)$, Current: $(A)$, Temperature: $(K)$ or $(0)$, and Amount of substance: $(A)\,(mol)$.

What are the kilogram equivalents for a Slug and a Pound ($lb$), and what is the Chandra Shekher Limit?

$1\,\text{Slug} = 14.57\,kg$, $1\,\text{Pound} = 0.4536\,kg$, and the Chandra Shekher Limit ($CSL$) is $1.4$ time the mass of sun, the largest practical unit of mass.

According to the practical units section, what are the values for Barn, Acre, and Hectare?

$1\,\text{barn} = 10-28\,m^2$, $1\,\text{acre} = 4047\,m^2$, and $1\,\text{hectare} = 10"\,m^2$.

Name the two Supplementary Quantities and provide the formula for Solid angle ($W$).

The quantities are Plane Angle (unit: Radian) and Solid Angle (unit: Steradian). The formula for Solid angle is $W = \frac{\text{Area}}{(\text{Radius})^2}$.

Define $1\,\text{Steradian}$ and provide the value of $1\,\text{Radian}$ in degrees.

$1\,\text{Steradian}$ occurs when the area taken is equal to the square of the radius; $1\,\text{Radian} = \frac{180^{\circ}}{\pi} \approx 57.3^{\circ}$.