Important Points on Elasticity for JEE Main 2015 by ednexa.com

1. Elasticity
Important points
1. Deformation
The change in the size and/or shape of a body is called deformation and the
external force producing the deformation is called the deforming force.
2. Types of Bodies
a. Elastic Bodies: They regain their original size and shape, when the deforming
forces are removed.
E.g. Metals like steel, copper
b. Plastic Bodies: They do not regain their original size and shape. When the
deforming forces are removed they retain the deformed shape.
E.g. plasticine, wax, butter
c. Rigid bodies cannot be deformed.
3. Stress
Internal Restoring Force (F) per unit area of cross-section.
2
1 1 2
2
t
F
stress SI unit (N/m )
A
Stress L MT
F Mg
For a wire,tensilestress ;
A r
volume stress dP change in pressure
Tangential Force F
Shearing stress
Area A
4. Strain
e dv
Tensile strain . Bulk (volume) strain
L V
Shearing strain( )
Lateral displacement of a layer
Perpendicular distance of the layer from the fixed layer
Strain has no units and dimensions.

2. 5. Hooke’s Law
Stress
Constant within elastic limit
Strain
This constant is called the modulus of elasticity.
6.
Longitudinal stress
Young's modulus Y
Longitudinal strain
2
2
F / A Mg/ r MgL
e/L e/L r e
7.
volume stress Vdp
Bulk Modulus(K)
volume strain dv
8. shearing stress Ft
Rigidity Modulus( )
shearing strain A
Where Ft is the component of the force, tangential to the area.
SI unit of y, k and n is N/m2
9.
D
Lateral strain D Poisson'sratio( )
Longitudinal strain L
L
It has no units and dimensions. Its limiting values are -1 to 0.5.
10. Work done in stretching a wire or strain energy stored in the wire
is given by
2
1 2
1 1 1 YA
W load extension F
2 2 2 L
1
W Average force extension (F F )
2
 


3. 11. Work done (or strain energy) per unit volume
2
2
1
stress strain
2
1 (stress) 1
(strain) Y
2 Y 2
12. 1 2
P.E. stored in a spring Kx
2
13. Useful Points
i. Thermal Stress: If there is a fall in temperature (θ), then a wire fixed between
two rigid supports tries to contract and tensile stress is developed. It is
called thermal stress. If α is the coefficient of linear expansion, then
Thermal stress= Y α θ
ii. Y is determined by using Searle’s method. The graph of extension against
load (or mass) is straight line. Form this graph we get the proportional limit,
elastic limit, yield point and breaking point. We can also find the ductile and
brittle metals.
iii. For rubber, the stress-strain graph is not linear. A large strain is produced
for a small stress. Rubber is an elastomer.