The work done on the body be zero under following situation using formula `W = fd cos theta `
(1) Work done is zero when the force .As for example , a block moving on a smooth horizontal table is not acted upon by a horizontal force but may undergo a large displacement .
(2) There is no displacement of body even the force is exerted on it . As for example , when one push hard against a rigid brick wall , the force exert on the wall does not work .
(3) When force and displacement are mutually perpendicular .
For example , during uniform circular motion , the displacement of the body is always along tangent of the circle and the force acting on the body is always towards the centre of circle so force and displacement is perpendicular to each other . In this situation work done by centripetal force is zero .
(4) (a) When more than one force acts on body and the net force of all these forces is zero then work done is zero .
For example : A cylinder is vertically tug with string as shown in figure . Gravitational force of earth acting on the cylinder and hence tension in teh string acting in upward direction but here displacement of cylinder is zero so work done is also zero .
(b) A sphere is placed in a V - shaped ditch as shown in figure (c ). There are three forces acting on it . Even though it doesn.t move . So the displacement by every force is zero and hence total work is also zero .
