A copper strip of $$200$$ $$mm$$ width and $$30$$ $$mm$$ thickness is to be rolled to a thickness of $$25$$ $$mm.$$ The roll of radius $$300$$ $$mm$$ rotates at $$100$$ $$rpm.$$ The average shear strength of the work material is $$180$$ $$MPa.$$ The roll strip contact length and the roll force are

A solid cylindrical stainless steel work piece of $$200mm$$ diameter and $$150mm$$ height. This component is reduced by $$50\% $$ in height with flat die in open die forging. Assuming the flow stress of the material as $$1000$$ $$MPa$$ and the coefficient of friction to be $$0.2,$$ the estimated forging force at the end of the stroke is

Consider the following statements:
In comparison to hot working, in cold working,
$$1.$$ Higher forces are required
$$2.$$ No heating is required
$$3.$$ Less ductility is required
$$4.$$ Better surface finish is obtained.

Which of the statements given above are correct?

Assertion (A) : Cold working of metals result in increase of strength and hardness.
Reason (R) : Cold working reduces the total number of dislocations per unit volume of the material.