Convert 20 dyne to Netwon using the dimensional method.
1 Answer
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
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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:
\(N_2=N_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c\)
\(=20\left[\frac{1g}{1kg}\right]^1\left[\frac{1cm}{1m}\right]^1\left[\frac{1s}{1s}\right]^{-2}\)
\(=20\left[\frac{1g}{1000g}\right]^1\left[\frac{1cm}{100cm}\right]^1\left[\frac{1s}{1s}\right]^{-2}\)
\(\therefore N_2=20\times10^{-5}=2\times10^{-4}\)
- 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,