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`        A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a, b and L`
5 years ago 396 Points
```							Sol. . ρ = mass/length = a+ bx
(a) S.I. unit of ‘a’ = kg/m and SI unit of ‘b’ = kg/m2 (from principle of homogeneity of dimensions)
(b) Let us consider a small element of length ‘dx’ at a distance x from the origin as shown in the figure.
∴ dm = mass of the element = ρ dx = (a + bx) dx
So, mass of the rod = m = ∫ dm = ∫_0^L〖(a+bx)〗  dx = [ax+(bx^2)/2]_0^L = aL + (bL^2)/2

```
5 years ago
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