Answer
Since the string's tension acts at a $90^{\circ}$ to the direction of motion, the string does no work on the plane.
Work Step by Step
Let $T$ be the tension in the string. We can find the work done by the string on the plane:
$Work = T~d~cos~\theta$
$Work = T~d~cos~90^{\circ}$
$Work = 0$
Since the string's tension acts at a $90^{\circ}$ angle to the direction of motion, the string does no work on the plane.
