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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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detailed solution

Correct option is B

In the given equation [ρ]=[b][x] ; ∴[b]=[ρ]/[x]. But ρ is mass per unit length and x is distance, therefore [b]=ML-1/L=ML-2 T0

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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+bx. What should be the dimensions of b?

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Ready to Test Your Skills?

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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?