If dimensions of critical velocity v_c of a liquid flowing through a tube are expressed as [^x ρ^y r^z] , where , ρ and r are the coefficient of visco - Physics MCQ Physics | ExamTest.live

hardMCQPhysicsPhysics

1 mark

If dimensions of critical velocity v_{c} of a liquid flowing through a tube are expressed as [η^{x} ρ^{y} r^{z}], where η, ρ and r are the coefficient of viscosity, density of liquid and radius of the tube respectively, then the values of x, y and z are:

A $1, 1, 1$
B $1, - 1, - 1$
C $- 1, - 1, 1$
D $- 1, - 1, - 1$

Solution & Step-by-step Explanation

Dimensions: v_{c} = [L T^{- 1}] η = [M L^{- 1} T^{- 1}] ρ = [M L^{- 3}] r = [L] $ [L T^{- 1}] = [M L^{- 1} T^{- 1}]^{x} [M L^{- 3}]^{y} [L]^{z} $ [M^{0} L T^{- 1}] = [M^{x + y} L^{- x - 3 y + z} T^{- x}] Comparing T : - 1 = - x \Rightarrow x = 1 .Comparing M : x + y = 0 \Rightarrow y = - x = - 1 .Comparing L : - x - 3 y + z = 1 \Rightarrow - 1 - 3 (- 1) + z = 1 \Rightarrow - 1 + 3 + z = 1 \Rightarrow z = - 1 .Values: 1, - 1, - 1 .

Practice this question

Try it yourself before checking the explanation above.

If dimensions of critical velocity v_{c} of a liquid flowing through a tube are expressed as [η^{x} ρ^{y} r^{z}], where η, ρ and r are the coefficient of viscosity, density of liquid and radius of the tube respectively, then the values of x, y and z are:

1, 1, 1

1, - 1, - 1

- 1, - 1, 1

- 1, - 1, - 1

Share This Question

fluid mechanics dimensional analysis

Related Questions

mediumMCQ

Consider a water tank as shown in the figure. It has one wall at x = L and is very wide in the z direction. When filled with a liquid of surface tension S and density ρ , the liquid surface makes an angle θ_0 ( θ_0 1 ) with the x -axis at x = L . If y(x) is the height of the surface, then the equation for y(x) is:(Take θ(x) ≈ θ(x) ≈ θ(x) = dy/dx and g as acceleration due to gravity) ![image](https://pub-7faa453bd1ec4bf0a04cc031c6f058de.r2.dev/images/e48999a7-2b29-4d5c-be16-ae2fd5fbcea5.png)

mediumMCQ

A microscope has an objective of focal length 2 cm , eyepiece of focal length 4 cm and the tube length of 40 cm . If the distance of distinct vision of eye is 25 cm , the magnification in the microscope is:

mediumMCQ

An electron (mass 9 × 10^-31 kg and charge 1.6 × 10^-19 C ) moving with speed c/100 ( c = speed of light) is injected into a magnetic field B of magnitude 9 × 10^-4 T perpendicular to its direction of motion. We wish to apply a uniform electric field E together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = 3 × 10^8 ms^-1 ):

mediumMCQ

There are two inclined surfaces of equal length ( L ) and same angle of inclination 45^ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction ( μ_k ) between the object and the rough surface is close to:

mediumMCQ

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying breaks, car A stops after 1000 m and car B stops after 1500 m . If F_A and F_B are the forces applied by the breaks on cars A and B, respectively, then the ratio F_A/F_B is:

hardMCQ

A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e) where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ( m is the mass of the electron):

Ready for a Full Test?

Practice with timed mock tests and track your performance across Physics.

Browse Tests Leaderboard

If dimensions of critical velocity $v_{c}$ of a liquid flowing through a tube are expressed as $[η^{x} ρ^{y} r^{z}]$ , where $η, ρ$ and $r$ are the coefficient of viscosity, density of liquid and radius of the tube respectively, then the values of $x, y$ and $z$ are:

Solution & Step-by-step Explanation

Practice this question

Share This Question

Related Questions

Ready for a Full Test?

Discussion

If dimensions of critical velocity vc​ of a liquid flowing through a tube are expressed as [ηxρyrz], where η,ρ and r are the coefficient of viscosity, density of liquid and radius of the tube respectively, then the values of x,y and z are:

Solution & Step-by-step Explanation

Practice this question

Share This Question

Related Questions

Ready for a Full Test?

Discussion

If dimensions of critical velocity $v_{c}$ of a liquid flowing through a tube are expressed as $[η^{x} ρ^{y} r^{z}]$ , where $η, ρ$ and $r$ are the coefficient of viscosity, density of liquid and radius of the tube respectively, then the values of $x, y$ and $z$ are: