Define Hooke’s law. Define three types of elastic modulus (Young’s Modulus, Bulk
Modulus & Rigidity Modulus) with formulae?

theja, 9 years ago

Grade:9

1 Answers

Aarti Gupta

askIITians Faculty 300 Points

9 years ago

Hooke's law states that the force F needed to extend or compress a spring by some distance

is proportional to that distance. That is:

where

is a constant factor characteristic of the spring, its stiffness.

· Young's Modulus of elasticity

Iti It is defined as the ratio of normal stress to the longitudinal strain within elastic limit.

F is the normal force applied at the end of its wire, A is area of cross section (= pr²), Dl is the extension produced due to normal force, L is the original length of the wire.

· Bulk Modulus of elasticity (K)

It is defined as the ratio of normal stress to the volumetric strain within the elastic limit.

Thus,

· Consider a spherical solid body of volume V and surface area a, when a force F is applied normally, the volume decreases by

Modulus of Rigidity

· It is defined as the ratio of tangential stress to the shearing strain within the elastic limit.

· Considering a solid metal cube whose lower face is fixed and its upper face is subjected to a tangential force F. The body suffers a change in its shape but not in its volume. If q is angle through which upper layer is sheared then,

(Modulus of Rigidity)

Thanks & regard

Aarti Gupta

askiitians Faculty