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

A particle with position vector $$\overrightarrow{\mathrm{r}}$$ has a linear momentum $$\overrightarrow{\mathrm{P}}$$. Which one of the following statements is true in respect of its angular momentum 'L' about the origin?

A child is standing with folded hands at the centre of the platform rotating about its central axis. The kinetic energy of the system is '$$K$$'. The child now stretches his arms so that the moment of inertia of the system becomes double. The kinetic energy of the system now is