The work done by the tension in the string when lifting an object of mass M at a constant acceleration of g/9 over a distance L is calculated as W = (10Mg/9) × L, including both the work done against gravity and the additional work to accelerate the mass.
The student is asking how much work is done by the tension in the string when an object of mass M is raised vertically with a constant acceleration of g/9. Assuming the distance the object is lifted is L, the work done by tension can be calculated using the equation for work, which states that work (W) is equal to force (F) times distance (d).
If the object accelerates at g/9 then the net force acting on the object is Mg/9. However, the tension must also support the weight of the object (Mg), the total tension in the string is 10Mg/9. The work done by tension as it lifts the object through distance L is thus W = (10Mg/9) × L.