Question

convert 5 joule into erg using dimensional analysis
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Answer 1

Answer:

5 joules =

5 joules =50000000 ergs.

5 joules =50000000 ergs. mark as brainlist answer

Answer 2

Concept: SI unit of work is joule and CGS unit of work is erg. We have to change SI system into CGS system using dimensional analysis. Dimension analysis shows the relationship of units of measurement and dimensons.

Dimension formula of Joule is $M^{} L^{2}T^{-2}$

Given: By comparing powers with $M^{a} L^{b}T^{c}$

we get, $a = 1, b=2, c = -2$

$M_{1} = 1 kg,\ M_{2} = 1 gm\\L_{1} = 1 m,\ L_{2} = 1 cm\\T_{1} = 1 sec,\ T_{2} = 1 sec\\n_{1}=5$

Find: $n_{2} = ?$

Solution:

Representation of physical quantity of system 1 is

$n_{1} [M_{1}]^{a} [L_{1}]^{b}[T_{1}]^{c}$

Representation of physical quantity of system 2 is

$n_{2} [M_{2}]^{a} [L_{2}]^{b}[T_{2}]^{c}$

By comparing,

$n_{1} [M_{1}]^{a} [L_{1}]^{b}[T_{1}]^{c} =n_{2} [M_{2}]^{a} [L_{2}]^{b}[T_{2}]^{c}$

$n_{2}=\frac{n_{1} [M_{1}]^{a} [L_{1}]^{b}[T_{1}]^{c}}{ [M_{2}]^{a} [L_{2}]^{b}[T_{2}]^{c}}$        

$n_{2}=n_{1}[\frac{M_{1} }{M_{2} } ]^{a} [\frac{L_{1} }{L_{2} } ]^{b} [\frac{T_{1} }{T_{2} } ]^{c}$    

$n_{2} =5[\frac{1kg}{1gm} ]^{1} [\frac{1m}{1cm} ]^{2} [\frac{1sec}{1sec} ]^{-2}$

$n_{2} =5[\frac{10^{3}gm }{1gm} ]^{1} [\frac{10^{2}cm }{1cm} ]^{2} [\frac{1}{1} ]^{-2}$    ⇔  $n_{2} =5$×$10^{3}$×$10^{4}$  ⇔  $n_{2} =5$×$10^{7}$erg

Therefore, $5 joule=5$×$10^{7}\ erg$

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