A circular hole is cut from a disc of radius 6 cm in such a way that the radius of the hole is 1 cm and the centre of 3 cm from the centre of the disc. The distance of the centre of mass of the remaining part from the centre of the original disc is

Options

A. `3/35 cm`
B. `1/35cm`
C. `3/10cm`
D. None of these

Answer

A

Explanation

For the calculation of the position of centre of mass, cut off mass is taken as negative. The mass of disc is

`m_(1)=pir_(1)^(2)sigma=pit^(2)sigma=36pisigma`
where `sigma`= surface mass density. The mass of cut of portion is
`m_(2)=pi(1)^(2)sigma=pi sigma`
`x_(cm)=(m_(1)x_(1)-m_(2)x_(2))/(m_(1)-m_(2))`
Taking origin at the centre of disc.
`x_(1)=0,x_(2)=3cm`
`x_(cm)=(36pisigmaxx0-pi sigmaxx3)/(36pisigma-pisigma)`
`=(-3pisigma)/(35pisigma)=-3/35cm`