Question

Convert MKS unit of work i.e. joule into CGS unit of work i.e. erg by using dimensional

analysis method.​

Answer 1

Explanation:

Joule : SI system, erg:CGS system

Work = Force x Distance = Mass x Acceleration x Length = Mass x

(Time)

2

Length

×

Length

Dimensions of work =

[W]=

[M

1

L

2

T

−2

]

∴ a= 1,b= 2,c= −2.

Now

SI system CGS system

M

1

=

1kg

M

2

=

1kg

L

1

=

1m

L

2

=

1cm

T

2

=

1s

T

1

= 1s

Here

N

1

1,N

2

=

?

∴ UsingN

2

=

N

1

[

M

2

M

1

] a

[

L

2

L

1

] b

[

T

2

T

1

] c

=

1

[

1g

1kg

]

1

[

1cm

1m

]

2

[

1s

1s

]

−2

=

1

[

1g

1000g

]

1

[

1cm

100cm

]

2

=

10

7

∴

N

2

10

7

So

1J=

10

7

erg