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Important questions on Dimensions And Dimensional Analysis

The dimensional formula for electric intensity is

A

B

C

D

View Answer

Since

The physical quantities not having same dimensions are:

A

Torque and work

B

Momentum and Planck's constant

C

Stress and Young's modulus

D

Speed and

View Answer

The torque and the work both have the same dimensions because they are given as the product of force and the distance.

.

On the other hand, the young's modulus is the ratio of stress and strain. The strain is a dimensionless quantity. Therefore, the unit of stress and young's modulus will be the same.

The unit of speed is and it has the dimension of .
The speed of light is given by:
Therefore, both will have the same dimensions.

So, option is correct.

The time dependence of a physical quantity is given by , where is a constant and t is time. Then constant is / has

A

Dimensionless

B

Dimensions of

C

Dimensions of P

D

Dimensions of

View Answer

must be dimension less in 

  

The potential energy of a particle varies with distance as , where A and B are constants. The dimensional formula for A x B is:

A

B

C

D

View Answer

Given,  
should have some dimension   

                

The pair of physical quantities, that have difference dimensions is 

A

Planck's constant and angular momentum

B

Energy density and pressure

C

Relative density and plane angle

D

Specific heat capacity and latent heat

View Answer

Planck's constant, symbolized h, relates the energy in one quantum (photon) of electromagnetic radiation to the frequency of that radiation.


Angular momentum Moment of inertia Angular velocity (Angular momentum)


So, here we can see that both the Planck's constant and Angular momentum have the same dimensions.

The dimensions of planck's constant equal to that of 

A

energy

B

momentum

C

angular momentum

D

power

View Answer

Planck's constant, symbolized , relates the energy in one quantum (photon) of electromagnetic radiation to the frequency of that radiation.


Angular momentum Moment of inertia Angular velocity (Angular momentum)


So, here we can see that both the Planck's constant and Angular momentum have the same dimensions.

Let us check the dimensional correctness of the relation .

View Answer

Here u represents the initial velocity, v the final velocity, a the uniform acceleration, and t the time.
The dimensional formula of u is .
The dimensional formula of v is .
The dimensional formula of at is .
Here the dimensions of every term in the given physical relation are the same, hence the given physical relation is dimensionally correct.

The dimensions of
are:

A

B

C

D

View Answer

We know that the speed of an electromagnetic wave is given by :

Therefore, has the dimension the same as that of the speed.

The dimensions of latent heat are - 

A

B

C

D

View Answer

  . . . . . . (1)

The dimensional formula of mass . . . . (2)

Also, the dimensions of heat dimensions of energy dimensions of work

Since, . . . . (3)

And, the dimensional formula of,

Displacement . . . (4)

Force  . . . (5)

On substituting equation (4) and (5) in equation (3) we get,

Work

Therefore, the dimensions of work or heat  . . . . (6)

On substituting equation (2) and (6) in equation (1) we get,

Or,

Therefore, latent heat is dimensionally represented as

The number of particles is given by crossing a unit area perpendicular to X-axis in unit time, where and are the number of particles per unit volume for the value of meant to and . Find the dimensions of called diffusion constant.

View Answer

no. of particle per unit area per unit time
no. of particle per unit volume
are distance from some reference point.

Dimension of 
Dimensional formula of  
Dimensional formula of 






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