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Grade -11 (NEB) > Science Physics Dimensional Analysis and Applications, Physical Quantities

Convert the unit from one to another using the dimensional method.

Convert 20 dyne to Netwon using the dimensional method.

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Solution:

Let, 20 dyne = N2 Newton

Here, dyne is the CGS unit and Newton is the SI unit of the force. The dimensional formula of force is [M L T-2], comparing this with [Ma Lb Tb]

So, a = 1, b = 1 and c = -2

Given System (CGS-Unit)

N1 = 20

M1 = 1g

L1 = 1 cm

T1 = 1 s

To be converted (SI-System)

N2 = ?

M2 = 1 kg

L2 = 1m

T2 = 1 s

Now, using the dimensional method of unit conversion, we have:

\(N_2=N_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c\)

\(=20\left[\frac{1g}{1kg}\right]^1\left[\frac{1cm}{1m}\right]^1\left[\frac{1s}{1s}\right]^{-2}\)

\(=20\left[\frac{1g}{1000g}\right]^1\left[\frac{1cm}{100cm}\right]^1\left[\frac{1s}{1s}\right]^{-2}\)

\(\therefore N_2=20\times10^{-5}=2\times10^{-4}\)

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Things to Remember From Physical Quantities

  • The four applications of dimensional analysis are:
    • To check the correctness of physical relation.
    • To derive the relation between various physical quantities.
    • To convert the value of physical quantities from one system of units into another system of units.
    • To find the dimensions of constants in the given equation.

  • The correctness of physical relation can be determined by comparing the dimension of the left-hand side (LHS) and the dimension of the right-hand side (RHS)
  • We can use the formula, \(N_2=N_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c\)\) to convert unit from one to another system using dimension.

  • Despite the usefulness of dimensions, there are some limitations. They are:
    • The dimensional analysis does not give any information about dimensionless constants.
    • If the quantity depends on more than three other physical quantities having dimensions, the formula cannot be derived.
    • We cannot derive the formula containing trigonometric functions, logarithmic functions, exponential functions, etc. It is best suited for linear functions only.
    • The exact form of a relationship cannot be determined when there is more than one part in any relationship.
    • It gives no information about the physical quantity,

 

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