Question

Which of these are correct?
{ see the attached picture }

Answer 1

Answer:

OPTION B and OPTION D are the correct answers .

Explanation:

The dimensional formula of ∈ is = Dimensional formula of charge / formula for force × ( distance dimensional formula )²  

Note that current = charge/time ⇒ charge = current×time ⇒ [ A T ]  

Dimension of ∈ = [ A T ]² / [ M L T⁻² ] [ L² ]

⇒ Dimension of ∈ =  [ M⁻¹ L⁻³ T⁴ A² ]

Dimension of n will be L⁻³ because it is the number per unit volume . Dimension of KB will be the dimension of energy or work because KB is the Boltzmann constant .  

Dimension of work = force × displacement

⇒ So dimension of KB = [ M L T⁻¹ ] × L  

⇒ Dimension of KB = [ M L² T⁻¹ ]  

Dimension of q will be that of a charge = [ A ]  

Now we have to put these values in the given options . I am solving only the required one as the answer will be very big and all the calculations cannot fit in a brainly answer .

For OPTION B ,  

√ [ ∈ KB T/ n q² ]  

⇒ √{ [ M⁻¹L⁻³T⁴A² ][ ML²T⁻¹ × T⁻¹ ] } / { [L⁻³A²T²]  }  

⇒ √[ L⁻¹T²A²]/[L⁻³A²T²]  

⇒ √{ [L² ] }  

⇒ [ L ]  

The dimension of the right hand side is equal to the dimension of the left hand side and hence the equation is dimensionally correct .

For OPTION D ,  

√ [ q² / ∈ n^{1/3} KB T ]  

⇒ √ [ A² /  { [ M⁻¹L⁻³T⁴A² ] [ L⁽⁻³⁾¹/³ ] [ ML²T⁻¹ × T⁻¹ ] }  

⇒ √ A² / { A² × L² × L⁻² × L⁻² }  

⇒ √ [ L² ]  

⇒ [ L ]  

The dimension of the right hand side is equal to the dimension of the left hand side and hence the equation is dimensionally correct .

NOTE :  

In real life , these dimensional formulas are useless . Dimensional formulas cannot even prove one thermodynamics / mechanics equation which has constants correct . Still don't know why we are taught all these outdated physics stuff . Thanks to the worst education system of the World _/\_ .

My opinion about our current syllabus is that our education system in India is just nowhere to compete against the World . We are taught useless things till class 10 and we do not know how to apply them in real life . The problem is that the basics of life starts from class 11 . Yes , I have studied till class 10 because of hatred . And now I will study as if every second is worth 1 million dollars . I will consider the studies more valuable than my life ....

Answer 2

Answer:

option b and d are correct