A wire of diameter 1, mm breaks under a tensi | vedclass

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(D) The breaking stress of a material is defined as the maximum force per unit area that the material can withstand before breaking. It is a constant

Vedclass · Accepted Answer

$4000$

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(D) The breaking stress of a material is defined as the maximum force per unit area that the material can withstand before breaking. It is a constant property of the material.Breaking Stress = $\frac{	ext{Breaking Force}}{	ext{Area of Cross-section}}$Breaking Force = $	ext{Breaking Stress} 	imes 	ext{Area} = 	ext{Breaking Stress} 	imes \pi r^2 = 	ext{Breaking Stress} 	imes \pi \left(\frac{d}{2}ight)^2$.Since the material is the same,the breaking stress is constant. Therefore,the breaking force is directly proportional to the square of the diameter $(F \propto d^2)$.Given: $d_1 = 1\, mm$,$F_1 = 1000\, N$,$d_2 = 2\, mm$.$\frac{F_2}{F_1} = \left(\frac{d_2}{d_1}ight)^2 = \left(\frac{2}{1}ight)^2 = 4$.$F_2 = 4 	imes F_1 = 4 	imes 1000\, N = 4000\, N$.

$A$ wire of diameter $1\, mm$ breaks under a tension of $1000\, N.$ Another wire,of the same material as that of the first one,but of diameter $2\, mm$ breaks under a tension of ...... $N$.

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