Final answer:
In a rope and pulley system with a mechanical advantage of 2, if a 12 N object is lifted 2 m, you need to pull 4 m of rope to perform this action.
Step-by-step explanation:
The question relates to mechanical advantage in a rope and pulley system. When the mechanical advantage of a system is 2 and the input force is 6 N with an output force of 12 N, it implies that the distance you have to pull the rope is twice the distance you lift the load because mechanical advantage is inversely proportional to the distance over which force is applied. Since the object is lifted 2 m, you need to pull 4 m of rope to lift it this distance.
In this case, the correct answer is d) 4m. To find the length of rope you need to pull, you can use the equation that relates the input distance and the output distance through the mechanical advantage (IMA) of the system:
Mechanical Advantage (IMA) = output force / input force = input distance (rope length) / output distance (load lift).
Given IMA = 2, and the output distance is 2 m, input distance = IMA × output distance = 2 × 2 m = 4 m.