$ ABC$  is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}, I_{CA}$  are the moment of inertia of the plate about $AB, BC$  and $CA$  respectively. Which one of the following relations is correct

If the density of material of a circular plate and a square plate as shown is same, the centre of mass of the composite system will be 

Two points of a rigid body are moving as shown. The angular velocity of the body is: ?

The centre of mass of two masses $m$ and $m'$ moves by distance $\frac {x}{5}$ when mass $m$ is moved by distance $x$ and $m'$ is kept fixed. The ratio $\frac {m'}{m}$ is

In free space, a shell moving with velocity $60\,m/s$ along the positive $x$ -axis. When it  passes through origin, it explodes into two peices of mass ratio $1 : 2.$ After the  explosion, the velocity of the centre of mass is ........ $m/s$.

A wheel of mass $10\,kg$ has a moment of inertia of $160\,kg-m^2$ about its own axis. The radius of gyration is ........ $m.$