Question

Wire can be broken by applying a load of 20 kg weight. the force required to break the wire of twice the diameter is

Answer 1

F α r
if radius is doubled, the force should be applied also be doubled.
r=2r¹.
d=2r.
d¹=2(2r¹)
d¹=4r¹
when d=2r, F=20.
now, d¹=4r¹ F¹=2(20)
:. the required Force F¹=40 kg weight..
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Answer 2

Answer:

Force to break wire = 80 kg

Step by step explanations :

Given that,

A wire can be broken by applying a load of 20 kg wt

here,

force = 20g

= 200N

let the force be F1

and the radius of the wire be r1

now,

diameter of the wire is doubled,

so,

thickness will also doubled,

on,

we know that,

Breaking stress is the characteristic of the material hence for two wires of same material having different thickness.

so,

let the force applied by the other mass on the wire of double diameter be F2

and radius of new wire be r2

now,

we know that,

ratio of force and square of radius of the 1st wire will equal to the force and square of radius of the second wire.

so,

F1/r1² = F2/r2²

here,

F1 = 200 N

r2 = 2r1

putting the values,

200/r1² = F2/r2²

200/r1² = F2/(2r1)²

200/r1² = F2/4r1²

800r1² = r1²F2

F2 = 800 N

so,

Force in kg weight = 80 kg