Question

No work is done by a force on an object if

• A. The force is always perpendicular to its velocity
• B. The force is always perpendicular to its acceleration
• C. The object's center of mass is stationary but the point of application of the force moves on the object
• D. The object moves in such a way that the point of application of the force remains fixed

Answer 1

Answer: (A), (C), (D)

The force is always perpendicular to its velocity
The object's center of mass is stationary but the point of application of the force moves on the object
The object moves in such a way that the point of application of the force remains fixed

$W=\int F.ds$
So, motion of both object and point of application of force on the object is necessary in order to keep $ds$ non zero.

Also angle between force and displacement( velocity ) should not be ${90}^0$ to keep dot product non zero.