Convert 10 J into erg
1 Answer
Solution:
Let, 10 Joules = N2 erg
Here, Joule is the SI unit of energy and erg is the CGS unit of energy. The dimensional formula of energy is [ M L2 T-2 ], comparing this with [ Ma Lb Tc ], we get
a = 1, b = 2 and c = -2
|
Given System (SI-Unit) N1 = 10 M1 = 1 kg L1 = 1m T1 = 1 s |
To be converted (CGS-System) N2 = ? M2 = 1g L2 = 1cm T2 = 1s |
Now, using the dimensional method of unit conversion, we have
\(\(\therefore N_2=N_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c\)
= \(10\left[\frac{1kg}{1g}\right]^1\left[\frac{1m}{1cm}\right]^2\left[\frac{1s}{1s}\right]^{-2}\)
= \(10\left[\frac{1000g}{1g}\right]^1\left[\frac{100cm}{1cm}\right]^2\left[\frac{1s}{1s}\right]^{-2}\)
∴ N2 = 108
Hence, 10 Joule = 108 erg
- 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,