Suppose A=B^nC^m, where A has dimensions, LT, B has dimensions L^2T^-1 and C has dimensions LT^2. Determine the dimensions of n and m values

Question

Suppose A=B^nC^m, where A has dimensions, LT, B has dimensions L^2T^-1 and C has dimensions LT^2. Determine the dimensions of n and m values.

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RI SƠ 1 year 2021-09-03T19:50:57+00:00 1 Answers 4 views 0

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    2021-09-03T19:52:20+00:00

    Answer:

    n = 1/5 and m = 3/5

    Explanation:

    The given quantity is :

    [tex]A=B^nC^m[/tex]

    Where

    The dimension of [A] = [LT]

    The dimension of [B] = [L²T⁻¹]

    The dimension of [C] = [LT²]

    We need to find the dimensions of n and m values.

    Using dimensional analysis,

    [tex][LT]=[L^2T^{-1}]^n[LT^2]^m\\\\\ [LT]=L^{2n}T^{-n}\times L^mT^{2m}\\\\\ [LT]=L^{2n+m}T^{2m-n}[/tex]

    Comparing both sides,

    2n+m=1 ….(1)

    -n+2m=1 ,…..(2)

    Solving (1) and (2), we get :

    n = 1/5 and m = 3/5

    Hence, this is the required solution.

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