Question

from a uniform circular sheet disc of radius 2cm(its centre of mass is at O), a circular portion of radius 1cm is removed such that shift in centre of mass is maximum. the disc is now rotated about O perpendicular to the plane through α, then the magnitude of displacement of new centre of mass is 1/√3 cm, then α is
Ans 120°

Answer 1

As $m_1\sdot b=m_2\sdot r$ where $b=$ OC, hence $b=\frac{m_2r}{m_1}=\frac{\pi\sdot r^2r}{\pi(R^2-r^2)}=\frac{r^3}{R^2-r^2}=1/3$ where $R=2cm$ , OO'$=$ $r=1cm$ , then the magnitude of displacement CC' is $CC'=\sqrt{b^2+b^2-2b^2\cos\alpha}=(2/3)\sin\alpha/2$ . As $CC'=1/\sqrt3$ hence $\sin\alpha/2=\sqrt3/2$ hence $\alpha=120^0$