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

							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     







 
 











fcon