An object of mass $$1 \mathrm{~kg}$$ is allowed to hang tangentially from the rim of the wheel of radius R. When released from the rest, the block falls vertically through $$4 \mathrm{~m}$$ height in 2 seconds. The moment of inertia is $$1 \mathrm{~kg} \mathrm{~m}^2$$. The radius of the wheel $$\mathrm{R}$$ is

A record player is spinning at an angular velocity of $$45 \mathrm{~rpm}$$ just before it is turned off. It then decelerates at a constant rate of $$0.8 \mathrm{~rad} \mathrm{~s}^{-1}$$. The angular displacement is

A body of mass $$5 \mathrm{~kg}$$ at rest is rotated for $$25 \mathrm{~s}$$ with a constant moment of force $$10 \mathrm{~Nm}$$. Find the work done if the moment of inertia of the body is $$5 \mathrm{~kg} \mathrm{~m}^2$$.

A thin circular ring of mass ,$$M$$ and radius $$R$$ rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity $$\omega$$. Four small spheres each of mass $$m$$ (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be