Question

convert 100 joule into erg using dimensional analysis​

Answer 1

Answer:

10^9

Explanation:

Joule is the unit of the physical quantity work and dimension of work is ML^2T^-2

This means we have to convert 100 kg m^2/s^-2

to g cm^2/s^-2

APPLY THE FORMULA

n2=100[kg/g][m/cm]^2[s/s]^-2

n2=100[1000g/g][100cm/cm]^2[s/s]^-2

(g cancelled cm cancelled and s cancelled)

we get:

n2=[1000][100]^2[1/1]^-2

n2=100 x 1000 x 100 x 100

n2=10^9

ANS : 10^9

Answer 2

Given: 100 joules.

To find: 100 joules in erg using dimensional analysis​.

Solution:

• The dimensional formula of work is ML²T⁻².
• Its unit in S.I. system is 'joule' and in C.G.S. system is 'erg'.
• Let M₁, L₁, T₁ represent kilogram (kg), metre (m), second (s) and M₂, L₂, T₂ represent gram (g), centimetre (cm), second (s) respectively.
• Then, the units of work in S.I. and C.G.S. systems will be (M₁L₁²T₁⁻²) and (M₂L₂²T₂⁻²) respectively.
• If the numerical values of work are n₁ and n₂ respectively, then

        $n_{1} (M_{1} L_{1}^{2} T_{1}^{-2} ) = n_{2} (M_{2} L_{2}^{2} T_{2}^{-2} )$

        $n_{2} = n_{1} (\frac{M_{1}}{M_{2}} ) ( \frac{L_{1}}{L_{2}} )^{2} (\frac{T_{1}}{T_{2}} )^{-2}$

• Here, n₁ = 100.

        $n_{2} = 100 joule (\frac{kg}{g} ) ( \frac{m}{cm} )^{2} (\frac{s}{s} )^{-2}$

             $= 100 (\frac{1000 g}{g} ) ( \frac{100 cm}{cm} )^{2} (\frac{s}{s} )^{-2}$

             $= 10^{2} * 10^{3} * 10^{4} * 1$

             $= 10^{9} erg$

Therefore, 100 joule is equal to 10⁹ erg.