You anchor the rope at one end and arrange a moveable pulley to achieve a mechanical advantage of 2. By the time you have lifted the object 5m off the ground, how much rope have you pulled through the pulley?

You can achieve a 2:1 advantage with a single pulley by rigging the pulley to the load. This is usually not practical for lifting but can be used for pulling a load horizontally quite easily. Say you need to pull a vehicle out of a ditch. Attach a strong rope to a tree then feed it through a pulley attached to the stuck vehicle and then to a pulling vehicle. For every two meters the pulling vehicle moves, the other vehicle will move one meter thus doubling the pulling force.

Mechanical advantage is a ratio of output to input.
A mechanical advantage of 2 implies that twice
the output has been achieved for the input.
Pulling 10 meters of rope and gaining 5 meters
of lift means that the object will appear to have
half as much weight. Essentially, you have pulled
twice as much rope, but half as heavy for each tug.

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How do you rig a single pulley to give a mech advantage of 2?

Edit: Thanks Gnarlok for helping me remember my elementary school science, memory of which was apparently on vacation when I answered this one.

d) 10 metres.

but you knew that…………..