Question

Convert 5 joule to erg dimensional analysis

Answer 1

U must know the dimension of Joule then,

it is:

[M] [L]^2 [T]^-2

then,

1 J  = 1000 * 10000 * 1 gmcm^2/s^2 = 10^7 ergs

as for erg the unit is: gcm^2/s^2.

for 5 J  => 6*10^7 ergs.

Answer 2

as you know , $\textbf{Joule}$ is the S.i unit of energy , heat and work.

dimension formula can be written as $ML^2T^{-2}$

where M is mass , L is length and T is time .

in S.I or MKS system ,
unit of mass in kg , unit of Length in metre and unit of time in second.
e.g., 1 joule = (1kg)(1m)²/sec² = 1kgm²/sec² ....(1)

we have to convert 5 joule in erg
we know, erg is cgs system of energy, heat and work .
in cgs
unit of mass in gram, unit of length in cm and unit of time second.

so, 1 erg = (1gram)(1cm)²/sec² = 1gcm²/s²....(2)

make relation between equations (1) and (2),
1kg = 10³ g , 1m = 10² m
now, 1kgm²/sec² = 10³ × 10⁴ gcm²/s²
or, 1 joule = 10^7 erg
or, 5 joule = 5 × 10^7 erg

hence, 5 joule = 5 × 10^7 erg