JEE Main & Advanced Sample Paper JEE Main Sample Paper-45

  • question_answer
    The velocity v (in cm/s) of a particle is given in terms of time? (in second) by the equation\[v=at+\frac{b}{t+c}\] The dimensions of a, b and c are

    a b c
    \[[{{L}^{2}}]\] \[[T]\] \[[L{{T}^{2}}]\]

    a b c
    \[[L{{T}^{2}}]\] \[[LT]\] \[[T]\]

    a b c
    \[[L{{T}^{-2}}]\] \[[L]\] \[[T]\]

    a b c
    \[[L]\] \[[LT]\] \[[{{T}^{2}}]\]

    Correct Answer: C

    Solution :

                 Given,                         \[v=at+\frac{b}{t+c}\] or         \[[at]\,=[v]=[L{{T}^{-1}}]\] \[\therefore \]    \[[a]=\frac{[L{{T}^{-1}}]}{[T]}=[L{{T}^{-2}}]\] Dimension \[c=[t]=[T]\] (we can add quantities of same dimensions only). \[\left[ \frac{b}{t+c} \right]=[v]\,=[L{{T}^{-1}}]\] or         \[[b]=[L{{T}^{-1}}]\,[T]=[L]\]

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