Question

using dimensions, show that 1 joule =10^7 ergs.​

Answer 1

Explanation:

ANSWER

It is given that 1joule=10

7

erg

Both erg and joule are the units of energy in CGS and MKS respectively. The dimensional formula of energy is [ML

2

T

−2

]

Let

1joule=Xerg

1[M

1

L

1

2

T

1

−2

]=X[M

2

L

2

2

T

2

−2

]

X=

[M

2

L

2

2

T

2

−2

]

[M

1

L

1

2

T

1

−2

]

X=[

M

2

M

1

][

L

2

L

1

]

2

[

T

2

T

1

]

2

X=[

gm

Kg

][

cm

m

]

2

[

s

s

]

−2

X=[

gm

1000gm

][

cm

100cm

]

2

(1)

−2

=(10)

3

(10

4

)

=(10)

7

So, 1Joule=10

7

erg