Explanation

(a) For the calculation of the position of centre of mass, cut off mass is taken as negative. The mass of disc is
$m_{1} = \pi r_{1}^{2}\sigma$
[image:7_image153.emf]
$= \pi(6)^{2}\sigma = 36\pi\sigma$
Where $\sigma$ is surface mass density
The mass of cutting portion is
$m_{2} = \ \pi(1)^{2}\sigma = \pi\sigma$
$x_{CM} = \frac{m_{1}x_{1} - m_{2}x_{2}}{m_{1} - m_{2}}$
Taking origin at the centre of disc,
$x_{1} = 0,x_{2} = 3$ cm
$x_{CM} = \frac{36\pi\sigma \times 0 - \pi\sigma \times 3}{36\pi\sigma - \pi\sigma} = \frac{- 3\pi\sigma}{35\pi\sigma} = - \frac{3}{35}cm$