Show that 1 joule = 10^5 erg
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Using dimension show that 1 joule =10
7
erg
Medium
Solution
verified
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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
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