Question

For the following dimensional equation, write the dimensional equations:

X ∝ = p^α q^β r^γ.

where [p] = ML^-1, [q] = L³, [r] = M⁴T^-1, and [X] = ML²T^-1

Answer 1

[p] = ML^-1, [q] = L³, [r] = M⁴T^-1, and [X] = ML²T^-1.

In case of M,

+ 4 =1

For L,

-+ 3=2

For T,

- =-1

Therefore,

=1

= -3

= -1/3

Therefore dimensional formula is,

X ∝ = p^-3 q^-1/3 r¹.