A force is applied on:

(i) a non-rigid body

(ii) a rigid body.

How does the effect of the force differ in the above two cases?

A force, when applied on a rigid object, does not change the inter-spacing between its constituent particles and therefore it does not change the dimensions of the object, but causes motion in it. On the other hand, a force, when applied on a non-rigid object, changes the inter-spacing between its constituent particles and therefore causing a change in its dimensions.