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Important questions on Dimensions And Dimensional Analysis

An unknown quantity  is expressed 
where = mass, = acceleration,   = length 
The unit of  should be 

A

meter

B

C

D

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First find unit of .


The value of log is dimensionless so dimension of:







Unit of  



Unit of

Match List I with List II and select the correct answer using the codes given below the lists:

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; ;

;











The velocity of a body moving viscous medium is given by where is time, and are constants. Then the dimensional formula of is:

A

B

C

D

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In  is the exponential term. So, the is  constant.
So, B has the dimensions as:


On the other hand, the dimension of will be the same as that of the velocity.
has dimensions as velocity


dimensional formula of A is

Find the dimensional formula for and :

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Since,
dimension of
Also we know that ,
this gives , dimension of  

Which of the following does not have the same dimension?

A

Electric flux, Electric field, Electric dipole moment

B

Pressure, stress, Youngs modulus

C

Electromotive force, Potential difference, Electric voltage

D

Heat, Potential energy, Work done

View Answer

B) Pressure:
    Stress :
    Youngs modulus : , here strain is dimension less So, all three has same dimension.

C) Electromotive force: 
     Potential difference: , with is same as Electromotive
     Electric voltage: If you see in a capacitor, then Voltage is given by 

D)  Heat:
      Potential energy: 
      Work done 

A) Electric flux:
     Electric field:

Hence, it has quantities with different units.

(here v = velocity, F = force, t = time)
Find the dimension of  and 

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dimensionless                 dimensionless  
So 

The Van der Waal's equation of moles of a real gas is

Where is pressure, is volume, is absolute temperature, is molar gas constant and are Van der Waal constants. The dimensional formula for is:

A

[]

B

[]

C

[]

D

[]

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Since, the dimensions of must be same as ,
Hence,


Also, dimension of must be same as that of . Hence, .

Thus,

Two forces and act at a point and have resultant . If is replaced by  acting in the direction opposite to that of , the resultant:

A

remains same

B

becomes half

C

becomes twice

D

none of these

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Pressure  (where  = Pressure F = force, v = velocity, t = time, x = distance)
State whether true or false: the above equation is dimentionally correct

A

True

B

False

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Pressure              (where  = Pressure F = force, v = velocity, t = time, x = distance)

Dimension of L.H.S           =  

Dimension of R.H.S. = 

Dimension of L.H.S. and R.H.S are not same So the relation cannot be correct Sometimes a question is asked which is beyond our syllabus, then certainly it must be the question of dimensional analyses

In the relation,  is pressure, is distance, is Boltzmann constant and  is the temperature. The dimensions of  will be 

A

B

C

D

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The dimension of power of e is zero.

Thus unit of:
Unit of boltzman's constant K is

By putting thes values we get,
Unit of

Therefore unit of

Unit of

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