Suppose A=BnCm, where A has dimensions LT, B has dimensions L2T-1, and C has dimensions LT2. Then the exponents n and m have the values?A. 2

Question

Suppose A=BnCm, where A has dimensions LT, B has dimensions L2T-1, and C has dimensions LT2. Then the exponents n and m have the values?A. 2; 3B. 2/3; 1/3C. 4/5; -1/5D. 1/2; 1/2E. 1/5; 3/5

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Tài Đức 5 years 2021-07-28T04:48:32+00:00 1 Answers 711 views 1

Answers ( )

  1. Neala
    0
    2021-07-28T04:49:40+00:00
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    Explanation:

    The expression is :

    A=B^nC^m

    A =[LT], B=[L²T⁻¹], C=[LT²]

    Using dimensional of A, B and C in above formula. So,

    A=B^nC^m\\\\\ [LT]=[L^2T^{-1}]^n[LT^2}]^m\\\\\ [LT]=L^{2n}T^{-n}L^mT^{2m}\\\\\ [LT]=L^{2n+m}T^{2m-n}

    Comparing the powers both sides,

    2n+m=1 …(1)

    2m-n=1 …(2)

    Now, solving equation (1) and (2) we get :

    n=\dfrac{1}{5}\\\\m=\dfrac{3}{5}

    Hence, the correct option is (E).

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