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A steel wire of diameter 2 mm has a breaking strength of 4 x 10^5 N. What is the breaking force of similar steel wire of diameter 1.5 mm?

A steel wire of diameter 2 mm has a breaking strength of 4 x 10^5 N. What is the breaking force of similar steel wire of diameter 1.5 mm? 

Grade:12

2 Answers

Aziz Alam IIT Roorkee
askIITians Faculty 232 Points
9 years ago
FBis directly proportional to the area (A)

FB’/FB=D’2/D2
\Rightarrow F_B'=F_B*D'^2/D^2=2.25*10^{5} N
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
 
SInce wires are of same material, the ultimate stress will be same for both
Now, force = stress x area
hence, force is directly proportional to area which in turn proportional to the square of diameter of wire.
Hence, F2/F1 = D22/D12
Hence, F2 = 4 x 105 x (1.5)2/(2)2
Hence, F2 = 2.25 x 105 N
 
Hope it helps.
Thanks and regards,
Kushagra

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