Choose the correct statement.

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(D) For pure rolling to occur,there must be a frictional force to provide the necessary torque to change the angular velocity. $(a)$ On a smooth horiz

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All of these.

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(D) For pure rolling to occur,there must be a frictional force to provide the necessary torque to change the angular velocity. $(a)$ On a smooth horizontal surface,there is no friction,so a sphere cannot initiate or maintain pure rolling if it starts with only translational motion. Thus,the statement is technically correct in the context of 'can it do' (it cannot). $(b)$ On a fixed smooth wedge,there is no friction to provide the torque required for pure rolling. Thus,it cannot perform pure rolling. $(c)$ Rolling friction is a complex phenomenon; depending on the deformation of the surface and the object,the resistive force can act in various directions relative to the motion. Since all statements describe physical limitations or properties correctly,the correct option is $(d)$.

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