A ring $\left(R\right)$ , a disc $\left(D\right)$ , a solid sphere $\left(S\right)$ and a hollow sphere with thin walls $\left(H\right)$ , all having the same mass but different radii, start together from rest at the top of an inclined plane and roll down without slipping. Then

Inner and outer radii of a spool are $r$ and $R$ , respectively. $A$ thread is wound over its inner surface and spool is placed ' over a rough horizontal surface. Thread is pulled by a force $F$ as shown in figure. In case of pure rolling, which of the following statements are false?

A horizontal plane supports a fixed vertical cylinder of radius $R$ and a particle is attached to the cylinder by a horizontal thread $AB$ as shown in figure. The particle initially rest on a horizontal plane. A horizontal velocity $v_0$ is imparted to the particle, normal to the threading during subsequent motion. Point out the false statements.

A stepped cylinder having mass $50\mathrm{k}\mathrm{g}$ and a radius of gyration $\left(\mathrm{K}\right)$ of $0.30\mathrm{m}$ . The radii $R_1$ and $R_2$ are respectively $0.6\mathrm{m}$ and $0.3\mathrm{m}$ . A pull $T$ equal to $200\mathrm{}\mathrm{N}$ is exerted on the rope attached to inner cylinder. The coefficient of static and dynamic friction between cylinder and ground are $0.1$ and $0.08$ respectively.

A plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to the right by a constant force $F$ . If the sphere does not slip over the plank, then