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NEET Sample Paper NEET Sample Test Paper-75

  • question_answer
    The position of a particle moving along x-axis depend on time in accordance with following equation\[\operatorname{x}=a{{t}^{2}}+b{{t}^{3}}\]. Then, dimensions of a and b are respectively

    A)  \[\left[ L{{T}^{-2}} \right];\,\, \left[ L{{T}^{-3}} \right]\]           

    B)  \[\left[ L{{T}^{-3}} \right];\,\, \left[ L{{T}^{-2}} \right]\]

    C)  \[\left[ L{{T}^{-2}} \right];\,\, \left[ L{{T}^{-2}} \right]\]           

    D)  None of these

    Correct Answer: A

    Solution :

    As, \[x = a{{t}^{2}}+ b{{t}^{2}}\] So, every term on RHS must have dimensions of x. \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a=\frac{X}{{{t}^{2}}}\Rightarrow \,\,[a]=[L{{T}^{-\,2}}]\] and       \[b=\frac{X}{{{t}^{3}}}\,\,\Rightarrow \,\,[b]=[L{{T}^{-\,3}}]\]


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