DIMENSIONS

 

Dimensions

It is discusses three fundamental dimensions in physics. All other dimensions are formed by using these three fundamental dimensions. Basic dimensions –

[Length] – L

[Mass] – M

[Time] – T

(But it is having other additional dimensions also, Temperature –θ

, Electric current – I, Intensity of light – L, number of moles – n)

 

If a physical quantity is given in square brackets, it represents a dimension of the quantity.

 

No dimensions for the quantities of units less.

Examples:

Index of refraction, strain, coefficient of friction, velocity ratio, efficiency, relative humidity, relative density

Note: however the plane angle and solid angle has units, they do not have dimensions.

The dimensions derived by using basic dimensions are called derived dimensions.

Example 1:

Dimension of velocity

Example 2: Dimension of momentum

 

Example 3: Dimension of heat capacity.

Example 4: Electric charge

 

 

 

 

Uses of Dimensions

1.   Test the accuracy of a formula

 

The relation among few physical quantities given in mathematical form by a formula. In a correct equation, the dimensions of the physical quantities on the sides of the equal sign should be equal to each other.

The relation among the three quantities of A, B, and C is when,

[Length] – L

[Mass] – M

[Time] – T

When some quantities are related as addition or subtraction, those adding or subtracting quantities should have equal dimensions.

When the relation among quantities is

When the relation is,

Further here,

 

The relations among dimensions also have for the units.

 

Example:

Show that the following equations are dimensionally correct.

 

 

 

2.   To find the dimension or units of a physical quantity or a constant

 

In a correct formula, the dimensions of the quantities of the two sides of equal sign is equal. Added or subtracted quantities of a formula has equal units. By using this matter we can find the dimensions or units of a quantity.

Example: If  are Pressure, Volume, number of moles and absolute temperature. Find the SI units of.

 

Example:

The rate of flowing heat through a uniform cross sectional metal rod,

What is the dimensions of conductivity (k)?

 

 

 

3.   Building up a relationship among few quantities

 

By analyzing dimensions among quantities, relations can be built up to maximum of 4 quantities. We cannot take the values of constants by this method.

 

Example:

It is assumed that the periodic time (T) of a simple pendulum is depend on the following quantities.

 

i.             Length of the pendulum()

ii.            Acceleration due to gravity (g)

iii.           Mass of the bob (m)

If the constant of proportionality is determined as, build a relation among these quantities.

Example:

The volume flow rate of a fluid through a horizontal hair tube turbulently in steady flow is depend on the following quantities.

i.             Radius of the tube(r)

ii.            Pressure gradient of the tube()

iii.           Coefficient of viscosity of the fluid ()

 

                          

Past Papers

2000 Paper I Problem 02

2002 Paper I Problem 01

2004 Paper I Problem 01

2005 Paper I Problem 01