A straight rod of length L has one of its end at the origin and the other at `X=L`. If the mass per unit length of the rod is given by `Ax` where A is constant, where is its centre of mass?

Options

A. L/3
B. L/2
C. 2L/3
D. 3L/4

Answer

C

Explanation

Mass per unit length
P= Ax
COM of rod
`= int rdm//int dm`
`= int_(0)^(1) x(Ax) dx//int_(0)^(1) Ax dx`
`= (A[(x^(3))/(3)]_(0)^(L))/(A ((x^(2))/(2))_(0)^(L))= (A(L^(3))/(3))/(A(L^(2))/(2))= (2L)/(3)`