The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is ………….

The ratio of the radii of gyration of a circular disc about a tangenti

1.	The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is ………….
Answer» `1:sqrt(2)` `1:3` `2:1` `sqrt(5):sqrt(6)` Solution :CIRCULAR Disc : Moment of inertia about `y_(1)` `I_(y_(1))=(MR^(2))/(4)` According to parallel AXIS theorem, Moment of inertia about `y._(1)` `IY._(1)=(MR^(2))/(4)+MR^(2)` `therefore Iy._(1)=(5)/(4)MR^(2)` ALSO `Iy._(1)=Mk_(1)^(2)` Circular ring : `Iy_(2)=(MR^(2))/(2)` According to parallel axis, Moment of inertia about `y._(2)` `Iy._(2)=(MR^(2))/(2)+MR^(2)` `therefore Iy._(2)=(3)/(2)MR^(2)` also `Iy._(2)=Mk_(2)^(2)` `therefore (k_(1)^(2))/(k_(2)^(2))=(I_(y._(1)))/(I_(y._(2)))=((5)/(4)MR^(2))/((3)/(2)MR^(2))` `therefore (k_(1)^(2))/(k_(2)^(2))=(5)/(6)` `therefore k_(1):k_(2)=sqrt(5):sqrt(6)`