Figure shows a composite body made up by welding a thin rod (of mass m and length r) normally at the centre P of a thin semicircular disc (of mass m and radius r). What are corrdinates of centre of mass of the system ?

Options

A. (0, 0)
B. `[(r )/(2), (2r)/(3)]`
C. `[r, ((2r)/(3pi) + (r )/(4))]`
D. `[r, ((2r)/(3pi) - (r )/(4))]`

Answer

D

Explanation

`y_(COM) = (m_(1)vec(y)_(1) + m_(2) vec(y)_(2))/((m_(1) + m_(2)))`
`= (m xx (4r)/(3pi) + m (-(r )/(2)))/(m + m)`
`y_(COM) = ((2r)/(3pi) - (r )/(4))`
`x_(COM) = r`