Question

If we choose velocity v, acceleration a, and force F as fundamental quantities, then what will be the dimensional formula for momentum?

Answer 1

Answer:

The velocity v, acceleration A and force For are chosen as fundamental quantities.

To find,

The dimensional formula of angular momentum in terms of v,A,F

Solution,

According to question,

L\propto v^xA^yF^zL∝v

x

A

y

F

z

or

L= v^xA^yF^zL=v

x

A

y

F

z

Putting the dimensional formula of L, v, A and F such that :

[ML^2T^{-1}]=k[LT^{-1}]^x{LT^{-2}]^y[MLT^{-2}

On comparing both sides of the above formula as :

z = 1 ........(1)

x + y + z = 2 ......(2)

-x -2y -2z = -1 ......(3)

On solving equation (1), (2) and (3) we get :

x = 3

y = -2

and z= 1

So, the dimensional formula of angular momentum is :

[L]=[v^3A^{-2}F][L]=[v

3

A

−2

F]

Hence, this is the required solution.

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