Question

Figure shows a uniform disc of radius R, from which a hole of radius $R/2$ has been cut out from left of the centre and right of the centre of disc also . Find the y coordinate of the Center of mass of the resulting disc?

• A. 1
• B. 2
• C. 0
• D. 3

Answer 1

The correct option is C 0

Mass of cut out disc on,

$\frac{M}{\pi R^2}\pi \left(\frac{R^2}{2}\right)=\frac{M}{4}$For x-coordinate

$x_{cm}=\frac{M{x}_1-m{x}_2+m{x}_3}{M-m+m}=\frac{M.0-\frac{M}{4}\left(\frac{R}{2}\right)+\frac{M}{4}\left(\frac{R}{2}\right)}{M-\frac{M}{4}+\frac{M}{4}}=\frac{R}{4}$

$y_{cm}=0$