Question

Convert 10^(-41) (N^2 * J^2) / kg^3 into (dyne^2 * erg^2)/gram^3 using dimension formula

Answer 1

N = newtons = force = M L T⁻²    in  kg-m/sec²
J = joule = energy = M L² T⁻²    in kg-m²/sec²
kg = M

erg = energy = M1 L1² T⁻²    in gm cm² /sec²
gm = M1
dyne = force = M1 L1 T⁻²  in gm cm/sec²

N = M L T⁻²  = 1000 M1 * 100 L1 * T⁻² = 10⁵ M1 L1 T⁻² = 10⁵ dyne
J = M L² T⁻² = 1000 M1 * (100 L1)  ² * T⁻² = 10⁷ erg
kg = 10³ gm

Quantity = 10⁻⁴¹ N² J² / kg³  = 10⁻⁴¹ * [ M L T⁻² ]²  [M L² T⁻²]² / M³
           = 10⁻⁴¹ * M L⁶ T⁻⁸
           = 10⁻⁴¹ * 1000 M1 * (100 L1)⁶ * T⁻⁸
           = 10⁻²⁵  M1 L1⁶ T⁻⁸
            = 10⁻²⁵ dyne² erg² / gm³