A thin rod of length `6 m` is lying along the x-axis with its ends at `x = 0` and `x = 6m`. It linear density (mass/length) varies with x as `kx^(4)`. Find the position of centre of mass of rod in meters.

Options

A.
B.
C.
D.

Answer

A

Explanation

`x_(cm) = (intxdm)/(intdm) = (int_(0)^(L) k ((x)/(L))^(n) xdm)/(int_(0)^(L) k ((x)/(L))^(n) dx) = ((n + 1)/(n + 2)) L`
For `n = 0, x_(cm) = (L)/(2)` and for `n rarr theta, x_(cm) = L`