Match List - I with List - II :List - IList - II(a) Mach number(i) Inertia force/Gravitational force(b) Froude number(ii) Inertia force/Elastic force(c) Nusselt number(iii) Momentum Diffusivity/Thermal Diffusivity(d) Prandtl number(iv) Convective heat transfer rate/Conductive heat transfer rateChoose the most appropriate answer from the options given below :

The correct matching is (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii).Mach number is the square root of inertia force over elastic (compressibility) force, \(V/c\) (a-ii).Froude number is the square root of inertia force over gravity force, \(V/\sqrt{gL}\) (b-i).Nusselt number is convective over conductive heat transfer, \(hL/k\) (c-iv).Prandtl number is momentum diffusivity over thermal diffusivity, \(\nu/\alpha\) (d-iii).Option C swaps Nusselt and Prandtl, and options A and D give the Mach number the Prandtl number's ratio, so only option B has all four right.

Dimensional Analysis and Similitude Questions and Answers

Q: A set of basic dimensions, mass, length, and time are represented by M, L, and T, respectively. What will be the dimensions of pressure in M-L-T system?

Pressure has dimensions \(ML^{-1}T^{-2}\).Pressure is force per unit area. Force is mass times acceleration, \(MLT^{-2}\), and area is \(L^{2}\):\[ [p] = \frac{MLT^{-2}}{L^{2}} = ML^{-1}T^{-2} \]\(MLT^{-2}\) is force itself, \(MLT^{-1}\) is momentum, and \(ML^{-1}T^{-1}\) is dynamic viscosity (Pa s).

Q: The basic dimensions, i.e., mass, length, and time are represented by M, L, and T, respectively. The correct dimension of dynamic viscosity is

The dimension of dynamic viscosity is \(ML^{-1}T^{-1}\).From Newton's law of viscosity, \(\tau = \mu\,du/dy\):\[ \begin{aligned} [\tau] &= \frac{MLT^{-2}}{L^{2}} = ML^{-1}T^{-2} \\ [du/dy] &= T^{-1} \\ [\mu] &= ML^{-1}T^{-1} \end{aligned} \]This matches the SI unit Pa.s, which is kg.m-1.s-1. \(MLT^{-2}\) is the dimension of force, and \(L^{2}T^{-1}\) is kinematic viscosity, \(\nu = \mu/\rho\), which has no mass dimension. \(L^{-2}T^{2}\) corresponds to no standard fluid property.

11.

A set of basic dimensions, mass, length, and time are represented by M, L, and T, respectively. What will be the dimensions of pressure in M-L-T system?

A.\(ML^{-1}T^{-2}\)
B.\(MLT^{-2}\)
C.\(MLT^{-1}\)
D.\(ML^{-1}T^{-1}\)

Exam Year(s)

GATE XE - 2024,

Answer: A

Pressure has dimensions \(ML^{-1}T^{-2}\).

Pressure is force per unit area. Force is mass times acceleration, \(MLT^{-2}\), and area is \(L^{2}\):

\[ [p] = \frac{MLT^{-2}}{L^{2}} = ML^{-1}T^{-2} \]

\(MLT^{-2}\) is force itself, \(MLT^{-1}\) is momentum, and \(ML^{-1}T^{-1}\) is dynamic viscosity (Pa s).

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12.

The basic dimensions, i.e., mass, length, and time are represented by M, L, and T, respectively. The correct dimension of dynamic viscosity is

A.\(MLT^{-2}\)
B.\(M^{0}L^{2}T^{-1}\)
C.\(ML^{-1}T^{-1}\)
D.\(M^{0}L^{-2}T^{2}\)

Exam Year(s)

GATE XE - 2026,

Answer: C

The dimension of dynamic viscosity is \(ML^{-1}T^{-1}\).

From Newton's law of viscosity, \(\tau = \mu\,du/dy\):

\[ \begin{aligned} [\tau] &= \frac{MLT^{-2}}{L^{2}} = ML^{-1}T^{-2} \\ [du/dy] &= T^{-1} \\ [\mu] &= ML^{-1}T^{-1} \end{aligned} \]

This matches the SI unit Pa.s, which is kg.m^-1.s^-1. \(MLT^{-2}\) is the dimension of force, and \(L^{2}T^{-1}\) is kinematic viscosity, \(\nu = \mu/\rho\), which has no mass dimension. \(L^{-2}T^{2}\) corresponds to no standard fluid property.

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13.

Match List - I with List - II :

List - I	List - II
(a) Mach number	(i) Inertia force/Gravitational force
(b) Froude number	(ii) Inertia force/Elastic force
(c) Nusselt number	(iii) Momentum Diffusivity/Thermal Diffusivity
(d) Prandtl number	(iv) Convective heat transfer rate/Conductive heat transfer rate

Choose the most appropriate answer from the options given below :

A.(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
B.(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
C.(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
D.(a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

Answer: B

The correct matching is (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii).

Mach number is the square root of inertia force over elastic (compressibility) force, \(V/c\) (a-ii).
Froude number is the square root of inertia force over gravity force, \(V/\sqrt{gL}\) (b-i).
Nusselt number is convective over conductive heat transfer, \(hL/k\) (c-iv).
Prandtl number is momentum diffusivity over thermal diffusivity, \(\nu/\alpha\) (d-iii).

Option C swaps Nusselt and Prandtl, and options A and D give the Mach number the Prandtl number's ratio, so only option B has all four right.

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