Q12 of 44 Page 5

If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula

According to question, momentum area and time are taken as fundamental quantities.


Now, we know that dimension of


Momentum(p)=


Area(A)=


Time (T)=


Energy=


Let us suppose,


E=


Now using principal of homogeneity, which states that the dimensions on both sides of a dimensional equation is same, we get


=




Equating the like terms we get


a=1, a+2b=2, -a+c=-2


1+2b=2, -1+c=-2


2b=1, c=-1


a=1, b=1/2, c=-1


Therefore,


E=


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