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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 $ρ$ , of this rod, varies as, $ρ = a + b x .$ What should be the dimensions of b?

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$M^{2} L^{1} T^{0}$

$M^{- 1} L^{2} T^{3}$

$M^{1} L^{- 2} T^{0}$

$M^{- 1} L^{3} T^{1}$

answer is B.

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Detailed Solution

In the given equation $[ρ] = [b] [x];$

$∴ [b] = \frac{[ρ]}{[x]} .$ But $ρ$ is mass per unit length and x is distance, therefore $[b] = \frac{M L^{- 1}}{L} = M L^{- 2} T^{0} .$

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