JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer 34) A rod of length L is placed on x - axis between \[x=0\] and \[x=L\]. The linear density i.e., mass per unit length denoted by p, of this rod, varies as, \[p=a+bx\]. What should be the dimensions of b?

    A)  \[{{M}^{2}}{{L}^{1}}{{T}^{0}}\]            

    B)  \[{{M}^{1}}{{L}^{-2}}{{T}^{0}}\]

    C)  \[{{M}^{-1}}{{L}^{3}}{{T}^{1}}\]           

    D)  \[{{M}^{-1}}{{L}^{2}}{{T}^{3}}\]

    Correct Answer: B

    Solution :

     In the given equation \[[\rho ]=[b][x];\] \[\therefore \]  \[[b]=[\rho ]/[x]\]. But \[\rho \] is mass per unit length and x is distance, therefore \[[b]=M{{L}^{-1}}/L=M{{L}^{-2}}{{T}^{0}}\] 0

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