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 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

The correct option is A the force is always perpendicular to its velocity

The work done by a force F in displacing a particle through d is:

$W=\overrightarrow{F}\cdot \overrightarrow{d}=Fd\cos \theta$

If $\theta ={90}^o$

$W=Fd\cos {90}^o=0$

Now direction of displacement is same as the direction of velocity.

So if force is always perpendicular to the velocity then no work is done.