Question

The lower surface of a cube is fixed. On its upper surface, force is applied at an angle of ${30^0}$ from its surface. The change will be in its:

(A) Shape
(B) Size
(C) Volume
(D) Both shape and size

Answer 1

Hint: Here force is applied only on the upper surface at a certain angle as given in the question above but the lower surface of the cube is fixed and it is asked what type of change is caused by this force in the cube. Force applied here will be normal stress and shear stress which will cause compression in the cube.



Complete answer:
According to the question, the force is applied on the upper surface and the lower surface is fixed. The applied force is at an angle of $30^{\circ}$.

When a force is applied to the cube, it moves parallel to the surface and compresses. As a result, its size will change.
Since the force direction is asymmetric, the compression will be asymmetric. As a result, its shape will change.
Therefore, we can say that when a force is applied, shear stress and normal stress act on the cube, compressing it. As a result, both shape and size have changed.
Normal stress, as the name implies, occurs when the direction of the deforming force is perpendicular to the cross-sectional area of the body. Shearing stress or tangential stress is the stress encountered by an object when the direction of the deforming force or external force is parallel to the cross-sectional area. This causes a change in the shape of the body.

In the above diagram, A represents normal stress acting on the surface whereas B represents shearing stress acting on the surface parallel to the cross-sectional area.
The correct option is (D).



Note: Whatever stress is applied, it only deforms the shape, not the volume. When stress is applied to an object, the molecules simply deform; no reaction occurs to increase the size of the molecules, and no external atoms or molecules are added, so there is only deformation. So, it is to be noted that volume will not change in the given question.