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