Question:
If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as $[\eta^x?^yr^z] \,$ where $\, \eta,?$ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by
If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as $[\eta^x?^yr^z] \,$ where $\, \eta,?$ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by
Updated On: Jul 12, 2022
- 1, -1 ,1
- 1,1,1
- 1,-1,-1
- -1, -1, -1
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The Correct Option is C
Solution and Explanation
$[v_c]=[\eta^x?^yr^z]$ (given) ... (i)
Writing the dimensions of various quantities in eqn. (i), we get
$[M^0LT^{-1}]=[ML^{-1}T^{-1}]^x[ML^{-3}T^0]^y[M^0LT^0]^z$
$\hspace20mm=[M^{x+y}L^{-x-3y+z}T^{-x}]$
Applying the principle of homogeneity of dimensions, we get
$\hspace10mm$x + y = 0; -x- 3y + z = 1; - x = -1
On solving, we get
$\hspace10mm$x =1,y = -1 , z =-1
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Concepts Used:
Units and Measurement
Unit:
A unit of a physical quantity is an arbitrarily chosen standard that is broadly acknowledged by the society and in terms of which other quantities of similar nature may be measured.
Measurement:
The process of measurement is basically a comparison process. To measure a physical quantity, we have to find out how many times a standard amount of that physical quantity is present in the quantity being measured. The number thus obtained is known as the magnitude and the standard chosen is called the unit of the physical quantity.
Read More: Fundamental and Derived Units of Measurement
System of Units:
- CGS system
- FPS system
- MKS system
- SI units
Types of Units:
Fundamental Units -
The units defined for the fundamental quantities are called fundamental units.
Derived Units -
The units of all other physical quantities which are derived from the fundamental units are called the derived units.