Question

Figure shows a composite system of two uniform rods of lengths as indicated. Then the coordinate of the center of mass of the system of rods are

A. `(L/2,2L/3)`
B. `(L/4,2L/3)`
C. `(L/6, 2L/3)`
D. `(L/6, L/3)`

Answer 1

Correct Answer - C
As rods are uniform therefore center of mass of both rods will beat their geometrical centers. The coordinates of CM of first rod `C_(1)` are (L/2,0) and second rod `C_(2)` are (0,L)

`therefore` `x_(CM) = (M(L/2) + 2M(0))/(M+2M) = L/6`
`y_(CM) = ((M(0) + 2M(L))/(M + 2M) = (2L)/3`
Hence, coordinates of CM are `(L/6, (2L)/3)`