A substance breaks down by a stress of 10⁶ N/m². If the density of the material of the wire is 3 x 10³ kg/m³, then the length of the wire of the substance which will break under its own weight when suspended vertically will be
Stress is the force applied per unit area of a material. It is a measure of how much force a material can withstand without breaking or deforming. Stress is typically expressed in pascals (Pa) and can be tensile compressive or shear depending on the type of force applied.
Chapter 8 of Class 11 Physics covers mechanical properties of solids such as stress strain and Hooke’s law. It explains Young’s modulus bulk modulus and shear modulus along with elastic potential energy. The chapter also discusses Poisson’s ratio and how materials respond to external forces. Understanding these concepts helps in analyzing material deformation.
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We can then use the formula for breaking stress to determine how long the wire will be under its own weight:
Breaking Stress = Force/ Area
Here, the force due to weight is given by:
Force = Weight = Density × Volume × g
Here,
Density = 3 × 10³ kg/m³
g = 9.8 m/s²
– Volume = A × L, where L is the length of the wire.
The breaking stress is a measure of the stress at which the wire will break so equate the force due to weight to the breaking stress, we get;
Breaking stress = Density × L × g
Rearranging to solve for L:
L = Breaking stress / (Density × g)
Substituting known values
L = (10⁶ N/m²) / (3 × 10³ kg/m³ × 9.8 m/s²)
L = 10⁶ / (3 × 10³ × 9.8)
L = 10⁶ / 2.94 × 10⁴ = 33.3 m
Therefore,
33.3 m
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