A) \[(4,-3,-2)\]
B) \[(-4,-3,\text{ }2)\]
C) \[(4,3,2)\]
D) \[(-4,-3,-2)\]
Correct Answer: A
Solution :
: Equate dimensions/powers of M, L, T and\[\theta \]. Dimensions of\[\sigma =[\sigma ]=[M{{L}^{-3}}{{\theta }^{-4}}]\] \[[k]=[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]\] \[[h]=[M{{L}^{2}}{{T}^{-1}}]\] \[[c]=[L{{T}^{-1}}]\] Given: \[\sigma =A{{k}^{\alpha }}{{h}^{\beta }}{{c}^{\gamma }}\] \[[M{{T}^{-3}}{{\theta }^{-4}}]={{[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]}^{\alpha }}{{[M{{L}^{2}}{{T}^{-1}}]}^{\beta }}{{[L{{T}^{-1}}]}^{\gamma }}\] From M, \[1=\alpha +\beta \] ...(i) From L, \[0=2\alpha +2\beta +\gamma \] ...(ii) From T, \[-3=-2\alpha -\beta -\gamma \] ...(iii) From \[\theta ,\]\[-4=-\alpha \] ...(iv) From (iv), \[\alpha =4\] ?.(v) From (i) and (v), \[\beta =-3\] ...(vi) From (ii), (v), (vi), \[\gamma =-2\] ...(vii) The set\[(\alpha ,\beta ,\gamma )\]is \[(4,-3,-2)\]You need to login to perform this action.
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