A disc of radius $$R$$ and thickness $$\frac{R}{6}$$ has moment of inertia I about an axis passing through its centre and perpendicular to its plane. Dise is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is

A square lamina of side '$$b$$' has same mass as a disc of radius '$$R$$' the moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $$\frac{b}{R}$$ is

A solid sphere rolls without slipping on an inclined plane at an angle $$\theta$$. The ratio of total kinetic energy to its rotational kinetic energy is

Two discs of same mass and same thickness (t) are made from two different materials of densities '$$d_1$$' and '$$d_2$$' respectively. The ratio of the moment of inertia $$I_1$$ to $$I_2$$ of two discs about an axis passing through the centre and perpendicular to the plane of disc is