Manipal Engineering Manipal Engineering Solved Paper-2014

  • question_answer
    If L, C and R denote the inductance, capacitance and resistance respectively, the dimensional formula for \[a{{\cos }^{3}}\alpha +3a{{\cos }^{2}}\alpha \sin \alpha =n,\]is

    A) \[{{(m+n)}^{2/3}}+{{(m-n)}^{2/3}}\]                      

    B) \[2{{a}^{3}}\]

    C) \[2{{a}^{1/3}}\]                

    D) \[2{{a}^{2/3}}\]

    Correct Answer: B

    Solution :

    Given, \[N{{O}_{2}}\]and we know that frequency of LC circuits \[N{{O}_{2}}\] Here the dimension of LC is equal to\[=5\times 0.1022=0.511\] \[as-\frac{1}{2}\frac{d[B{{r}^{-}}]}{dt}=\frac{1}{3}\frac{d[B{{r}_{2}}]}{dt}]\]gives the time constant of L - R circuit, so that the dimension of \[-\frac{d[B{{r}^{-}}]}{dt}=\frac{5}{3}\frac{d[B{{r}_{2}}]}{dt}=\frac{5}{3}\times 0.025=0.042M{{s}^{-1}}\]is equal to [T]. Hence the required dimensions \[LiAl{{H}_{4}}\]


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