AP EAMCET Engineering 2011 Solved Paper

Let centre O1 of disc be the origin. Due to symmetry the centre of mass of remaining part will lie at x -axis. Let CM of new disc is at point O2 where, O1O2=αR(given).
here mass of cut off portion,m=

π(R)2.M

π(2R)2

=

M

4

and position of its centre of mass, O1O1=R
Hence, for remaining part (new disc)
xCM=αR=

M×0−( M 4 )×R

M− M 4

=−

R

3

⇒α=

1

3