Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of of a string.
1)In which case does the object have the biggest total work done on it by all forces during its motion?

Work done in all the three cases will be the same.

Explanation:

1) The free falling body has only one force acting on it, the gravitational force. The work done on the body = mgH (Gravitational potential energy)

2) There are two forces acting on the body going down on a frictionless inclined plane - gravity and the normal force. The gravitational potential energy will be the same. The work done due to the normal force is zero, since the direction of the force is perpendicular to the displacement. Hence, total work done on the body = mgH

3) In the case of the body swinging on the end of a string, the change in gravitational potential enrgy will once again be the same since difference in height is H. The additional force on the body is the tension due to the string. But the work done due to this force is zero, since the displacement of the body is perpendicular to the tension. Therefore, the total work done on the body is once again mgH.

d.7.5cm is your answer