state the formula, unit & dimensional formula for following terms a.,force b, power c, gravitational d,constant d,Torque e, surface tension.
Answers
Explanation:
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
Answer:
Explanation:Hello Dear.
(a) By using the newton law of gravitation,
We know,
F = G / r²
where G is the gravitational constant.
So by this formula , we get
G =
so now changing into dimensions.
∴ [G] = [F]L² /M² = MLT⁻².L² / M²
[G] = M⁻¹L³T⁻²
Hence the dimensional formula of universal constant of gravitation is M⁻¹L³T⁻²
_________________.
(b) Dimension of surface tension→
∵ S = ρgrh / 2
where
S = Surface Tension, ρ = Density, g = Acceleration due to gravity, h = Height
∴ changing into dimension , [S] = (ρ)(g) L²
[S]= × × L²
[S] = MT⁻²
Hence,we get the dimensional formula of surface tension =MT⁻² .
__________________
(c) Dimension of Thermal conductivity
∵ Q = [k A(θ₂ - θ₁)t] ÷ d
∴ k = Qd ÷ [A(θ₂ - θ₁)t]
Here Q is the heat energy , so the dimension of Q = [ML²T⁻²] ,
where A is the area t is the time & d is the thickness.
Now , K = [ML²T⁻² . L] / L².KT
K = MLT⁻³K⁻¹
Hence the dimension of thermal conductivity is MLT⁻³K⁻¹ .
_________________
(d) Dimension of coefficient of Viscosity .
F = η.A ×
where F is the force , now changing into dimension.
MLT⁻² = (η) L² ×
MLT⁻² = (η)
now , η = ML⁻¹T⁻¹
Hence dimensional of coefficient viscosity is ML⁻¹T⁻¹
___________
Hope it Helps.
