Test: Elastic moduli & Applications of Elastic behaviour of Materials (30 July) - JEE MCQ

The  law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid body i.e. stress = k x strain.

A body is said to be perfectly elastic when its coefficient of restitution is 1 or we observe total  reformation in the body. That means that whatever hits it doesn't lose any of its kinetic energy or once the body gets totally reformed after a collision.

Beyond the elastic limit, if still some force is applied to the body, at first the body deforms completely and when it can’t deform more, it starts to break into pieces. Now when the plastic range is small, on less extent of applied external force the body would break. And we know such objects are called brittle.

strain energy=1/2×stress × strain Work done by a force on a wire
W =2LAy(ΔL)²/2L
=1/2(yALΔ/L)ΔL
=1/2​(yΔL/L)(ΔL/L)(AL)
=1/2(Stress)(Strain)(Volume)
(Work)/(volume)=1/2*(stress)(strain)

From Hooke's Law: F = kx
The force on the spring is the weight of the object, 13.2*9.8 = 129 N
x = 5.93 cm = 0.0593 m
129 = (0.0593)x
x = 2175 N/m 

Stress is referred to as the applied strain over a unit area, and we know strain is the force acting along the line, which means strain and force have the same dimensions. Thus stress and pressure have the same dimensions too.
Dimension of Force =[MLT⁻²]
Dimension of Area = [M⁰L²T⁰]
Therefore, Dimension of Stress = [MLT⁻²]/[M⁰L²T⁰]
= [ML⁻¹T⁻²]
Dimension of pressure =[ML⁻¹T⁻²]

Young's Modulus of elasticity =stress/strain
Y= [F/a/△l/l] ​ or Y= [Fl​/a△l]
or △l= [Fl/aY] ​= Fl​/ πr²Y
In the given problem, △l∝ l​/ r²
When both l and r are doubled, △l is halved.

Same elastic properties in all direction is called the homogenity of a material.

Modulus of rigidity is defined as the ratio of Shear stress to shear strain.

F =AYΔl/L
Δl = FL/AY