• # 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)  ${{M}^{-1}}{{L}^{2}}{{T}^{3}}$

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