9702_s22_qp_13 Question 20

A steel wire has a length of 300 cm and a cross-sectional area of 0.50 mm² . The Young modulus of steel is 2.0 x 10¹¹Pa. 

One end of the wire is attached to a fixed point. A load of 10 N is hung from the other end. The wire obeys Hooke’s law. 

What is the extension of the wire? 

A 3.0 x 10^-7 m 

B 3.0 x 10^-5 m 

C 3.0 x 10^-4 m 

D 3.0 x 10^-2 m 

ANSWER: C

The Physics Behind answer

• One version of Hooke's Law states that stress [F/A] is proportional to strain [x/L], and that the proportionality constant is Young modulus [E] where F is force, A is area, L is original length, and x is the extension which is being asked in this question.

E = (F / A) / (x / L)

E = FL / xA

x = FL / AE

• The extension x therefore is

x = (30 N m) / 100 000 N

x = 0..0003 m

[option C]