Question

Assume that a block of very low shear modulus is fixed on an inclined plane as shown. Due to elastic forces it will deform. What will be the shape of the block ?

• A. A
• B. B
• C. C
• D. D

Answer 1

Answer: (A)

A

Answer 2

The block is on an inclined plane, so the component of gravity acting parallel to the incline is $mg \sin\theta$. This force tends to cause the block to slide down. Since the block is fixed at its base and has a very low shear modulus, it will deform due to this force. The deformation will be primarily shear deformation, where parallel layers of the material slide past each other. For a rectangular block with its base fixed on the inclined plane, the force $mg \sin\theta$ will cause the top surface of the block to displace parallel to the bottom surface, downwards along the incline. This results in the sides of the block tilting and the original rectangular shape deforming into a parallelogram (in 2D) or a sheared rectangular prism (in 3D). Option (A) depicts this shear deformation, showing the original rectangular shape (dashed lines) and the deformed shape (solid lines) where the top surface has moved downwards along the incline.