Question

if velocity v, acceleration A and force For are chosen as fundamental quantities , then the dimensional formula of angular momentum in terms of v,A,F would be what?​

Answer 1

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Answer 2

Given that,

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,

$L\propto v^xA^yF^z$

or

$L= v^xA^yF^z$

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

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

$[ML^2T^{-1}]=k[L^xT^{-x}][L^yT^{-2y}][M^zLT^{-2z}]\\\\[ML^2T^{-1}]=k[M^zL^{x+y+z}T^{-x-2y-2z}]$  

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 :

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

Hence, this is the required solution.

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Dimensional analysis

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