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Byju's Answer
Standard XII
Physics
Dimensional Analysis
Find the dime...
Question
Find the dimensional formulae of the following quantities:
1.
the universal constant of gravitational
G
2.
the surface tension
S
,
3.
the thermal conductivity
k
and
4.
the coefficient of viscosity
η
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Solution
Universal constant of gravitation
G
Gravitational Force
=
G
m
1
m
2
r
2
⇒
G
=
F
.
r
2
m
1
m
2
[
G
]
=
[
M
L
T
−
2
]
[
L
2
]
[
M
]
[
M
]
[
G
]
=
M
−
1
L
3
T
−
2
2) Surface tension
S
S
=
F
o
r
c
e
l
e
n
g
t
h
⇒
[
M
L
T
−
2
]
[
L
]
[
S
]
=
[
M
L
0
T
−
2
]
3) Thermal conductivity
K
Δ
Q
Δ
t
=
K
A
Δ
T
Δ
x
⇒
K
=
−
Δ
Q
Δ
t
×
Δ
x
Δ
T
×
1
A
K
=
e
n
e
r
g
y
t
i
m
e
×
l
e
n
g
t
h
t
e
m
p
e
r
a
t
u
r
e
×
1
A
r
e
a
=
M
L
2
T
−
2
T
×
L
K
×
1
L
2
[
K
]
=
[
M
L
T
−
3
K
−
1
]
4)
coefficient of viscosity
n
n
=
F
A
(
d
v
/
d
x
)
⇒
[
M
L
T
−
2
]
[
L
2
]
[
L
T
−
1
]
/
[
L
]
[
n
]
=
M
L
−
1
T
−
1
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