Identify the incorrect statement :

No work is done by a force F on an object if :

1. the object is stationary but the point of application of force moves on the object.
2. the object moves in such a way that the point of application of force remains fixed.
3. the force is always perpendicular to velocity.
4. the force is always perpendicular to acceleration.

the force is always perpendicular to acceleration.

Reason — Work done by a force is given by,

Work done = F S Cos θ

So, no work is done when the force is perpendicular to the displacement of the point of application.

Let us check the given statements:

1. If the object is stationary, there is no displacement of the object as a whole, so work done is taken as zero.
2. If the point of application remains fixed, there is no displacement of that point, so no work is done.
3. If force is always perpendicular to velocity, it is perpendicular to displacement, so no work is done.
4. Force perpendicular to acceleration is not the condition for zero work. In fact, from Newton's second law, acceleration is generally in the direction of force.

Hence, incorrect statement is "the force is always perpendicular to acceleration".