Answer

Verified

381.6k+ views

**Hint:**Learn about the different dimensions of the quantities that are given in the expression of the V here. The physical quantities given in the expression are the pressure, radius, coefficient of viscosity and length respectively. The dimension of any physical quantities are written in terms of mass length and time.

**Complete step by step answer:**

In the given expression the physical quantities given are P that is the pressure, r is the radius \[\eta \] is the coefficient of viscosity l is the length. Now, we know that the dimension of any physical quantities are written in terms of mass, length and time by the form \[[{M^x}{L^y}{T^z}]\] where, \[x,y,z\] are some constant for that particular quantity.

Now, we know that the dimension of pressure is, \[[{M^1}{L^{ - 1}}{T^{ - 2}}]\].

Also the dimension of radius is \[[L]\].

The dimension of coefficient of viscosity is \[[{M^1}{L^{ - 1}}{T^{ - 1}}]\]

And the dimension of length is \[[L]\].

We know that the constants are dimensionless quantities.

Hence, putting this dimensions in the given expression we can find the dimension of V as,

\[[V] = \dfrac{{[{M^1}{L^{ - 1}}{T^{ - 2}}]{{[L]}^4}}}{{[{M^1}{L^{ - 1}}{T^{ - 1}}][L]}}\]

Upon simplifying we will have,

\[[V] = [{M^{1 - 1}}{L^{ - 1 + 4 - 1 + 1}}{T^{ - 2 + 1}}]\]

\[\therefore [V] = [{M^0}{L^3}{T^{ - 1}}]\]

Hence the dimension of the term \[V\] is \[[{M^0}{L^3}{T^{ - 1}}]\].

**Hence, option B is the correct answer.**

**Note:**We can also determine the dimension of each quantity from analyzing the unit of the individual quantities. Especially for the coefficient of viscosity. We know that the unit of coefficient of viscosity is nothing but the \[Ns{m^{ - 2}}\]. In the unit newton is the unit of force and force is mass times acceleration like this. We can easily find the dimension of compound physical quantities if we can’t recall the dimension of each quantity.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which places in India experience sunrise first and class 9 social science CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE