# GATE (TF) Textile 2021 Question Paper Solution | GATE/2021/TF/17

###### Question 17 (Textile Technology & Fibre Science)

A textile filament records a tensile stress of 0.3 GPa at a tensile strain of 0.04. Assuming Hookean behavior, the tensile modulus (GPa) of the filament, (rounded off to one decimal place), is _7.5______.

write here

Formula:
Tensile modulus of the filament(GPa)=Tensile Stress/Tensile Strain
=0.3/0.04

### What is Hooke’s Law explain ?

Hooke’s Law is a principle in physics that describes the relationship between the deformation (stretching or compressing) of a solid material and the force applied to it. According to Hooke’s Law, the deformation of an elastic material is proportional to the force applied to it, as long as the material is within its elastic limit.
More specifically, Hooke’s Law states that the force F required to deform a material by a distance x is given by the equation:
F = -kx
where k is the spring constant of the material, which is a measure of its stiffness. The negative sign indicates that the force is in the opposite direction to the deformation.

### What is Hookean region ?

The Hookean region is the range of deformation of a material in which Hooke’s Law applies, meaning that the deformation is proportional to the applied force. In this region, the material behaves elastically and will return to its original shape and size once the force is removed. The Hookean region is limited by the yield point of the material, beyond which the material may undergo plastic deformation and permanent damage.