The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is $$2400 \mathrm{~g} \mathrm{~cm}^2$$. The length of the $$400 \mathrm{~g}$$ rod is nearly:

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is $$v$$ in the direction shown, which one of the following options is correct ($$P$$ and $$Q$$ are any highest and lowest points on the wheel, respectively)?

A constant torque of $$100 \mathrm{~N} \mathrm{~m}$$ turns a wheel of moment of inertia $$300 \mathrm{~kg} \mathrm{~m}^2$$ about an axis passing through its centre. Starting from rest, its angular velocity after $$3 \mathrm{~s}$$ is :-

The ratio of radius of gyration of a solid sphere of mass $$M$$ and radius $$R$$ about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-