Limitation of Dimensional Analysis
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Q. Test which of the following equations are dimensionally correct. (S = surface tension, 𝜌 = density, P = pressure, V = volume, η = coefficient of viscosity, 𝑟 = radius, v = velocity, 𝑡 = time, 𝑙 = length, H = height)
- H=2Scosθρrg
- v=√Pρ
- V=πρr4t8ηl
- All correct
Q. The Van Der Waal’s equation of state for some gases can be expressed as: (P+aV2)(V−b)=RT Where P is the pressure, V is the molar volume and T is the absolute temperature of the given sample of gas and a, b and R are constants.
The dimensional representation of ab/RT is
The dimensional representation of ab/RT is
- ML5T−2
- M0L3T0
- ML−1T−2
- None of these
Q. If x and a stand for distance, then for what value of n in the given equation is dimensionally correct? The equation is ∫dx√a2−xn=sin−1xa
- 0
- 2
- −2
- 1
Q.
The force F is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt. The dimensional formula of DB is
[M0L0T0]
[M0L0T−1]
[M0L−1T0]
[M0L1T−1]