19. Find the dimensional formulae for the following physical quantities: a) Torque b) Coefficient of Viscosity c) Voltage
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Answer:
Universal constant of gravitation G
Gravitational Force =G
r
2
m
1
m
2
⇒G=
m
1
m
2
F.r
2
[G]=
[M][M]
[MLT
−2
][L
2
]
[G]=M
−1
L
3
T
−2
2) Surface tension S
S=
length
Force
⇒
[L]
[MLT
−2
]
[S]=[ML
0
T
−2
]
3) Thermal conductivity K
Δt
ΔQ
=KA
Δx
ΔT
⇒K=−
Δt
ΔQ
×
ΔT
Δx
×
A
1
K=
time
energy
×
temperature
length
×
Area
1
=
T
ML
2
T
−2
×
K
L
×
L
2
1
[K]=[MLT
−3
K
−1
]
4) coefficient of viscosity n
n=
A(dv/dx)
F
⇒
[L
2
][LT
−1
]/[L]
[MLT
−2
]
[n]=ML
−1
T
−1
Verified answer
Answer:
Universal constant of gravitation G
Gravitational Force =G
r
2
m
1
m
2
⇒G=
m
1
m
2
F.r
2
[G]=
[M][M]
[MLT
−2
][L
2
]
[G]=M
−1
L
3
T
−2
2) Surface tension S
S=
length
Force
⇒
[L]
[MLT
−2
]
[S]=[ML
0
T
−2
]