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NEET Sample Paper NEET Sample Test Paper-83

  • question_answer
    The velocity v of a particle at time t is given by\[\nu =at+\frac{b}{t+c}\], where, a, b and c are constants. The dimensions of a, b and c are

    A)  \[[L],\,[LT]\,\,and\,\,[L{{T}^{-\,2}}]\]   

    B)  \[[L{{T}^{-\,2}}],\,\,[L]\,\,and\,\,[T]\]

    C)  \[[{{L}^{\,2}}],\,\,[T]\,\,and\,\,[L{{T}^{-\,2}}]\]          

    D)  \[[L{{T}^{-\,2}}],\,[LT]\,and\,[L]\]

    Correct Answer: B

    Solution :

    As, \[\operatorname{v}=\,\,at\,\,+\,\,\frac{b}{t+c}\] c can only be added to if it has same dimension at t, \[\therefore \,\,\,c=\left[ T \right]\] at must have dimension same as velocity i. e        \[at=\left[ L{{T}^{-}}^{1} \right] \Rightarrow \, a =\,\,\frac{[L{{T}^{-\,1}}]}{[T]}\,\,=\,\,[L{{T}^{-}}^{2}]\]


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