Workdone by a force on an object is zero, if

Work done by a force on an object is zero under the following conditions:

No Displacement: If the force is applied to an object, but the object doesn't undergo any displacement (i.e., it doesn't move), then the work done by the force is zero. This is because work is defined as the product of force and displacement, so if there is no displacement, the work done is zero.

Force Perpendicular to Displacement: If the force is applied to an object in a direction perpendicular to the direction of displacement, then the work done by the force is zero. This is because the component of the force that contributes to displacement is zero. Only the component of the force parallel to the displacement contributes to work.

Mathematically, the formula for work done by a force F over a displacement d is given by:

Work = F * d * cos(θ),

where θ is the angle between the direction of the force and the direction of displacement. If θ is 90 degrees (force perpendicular to displacement), the cosine of 90 degrees is 0, and thus the work done is zero.

It's important to note that if the force and displacement are in the same direction, the work done will be positive, and if they are in opposite directions, the work done will be negative.