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Materials

Q1. A sample of wire has a Young modulus E. When a force F is applied to it it extends by 10 mm

A second sample of wire made from an identical material has three times the length and half the diameter of the first sample.

What is the extension of the second wire if a force F is applied ot it?

A
2.5 mm
B
10 mm
C
60 mm
D
120 mm

 

ΔL = FL/AE 

ΔL∝ L

So, three times the length makes it 3ΔL

Diameter is related to area: A = ¼πd2

So ΔL ∝ 1/d2

1/½2 = 4

Halving the diameter makes it 4ΔL

Put together we get 12ΔL = 12 x 10mm

= 120 mm

Choice D

Q2. A sample of wire has a Young modulus E.

A second sample of wire made from an identical material has three times the length and half the diameter of the first sample.

What is the Young modulus of the second sample of wire in terms of E?

A
0.25E
B
E
C
6E
D
12E

E is a property of the material - both wires are of the same material and so will have the same Young Modulus!

Q3. What is the name given to a material that breaks without deformation when a force is applied to it?

A
Plastic
B
Brittle
C
Stiff
D
Elastic

 

Q4. What cannot be used as a unit for the Young modulus?

A
N m–2
B
Pa
C
kg m–2 s–2
D
kg m–1 s–2

Usual unit is N m–2 (choice A) or Pa (choice B)

But F = ma

so N = kg m s–2

therefore unit can be kg m s–2 x m–2 = kg m–1 s–2 (choice D)

Answer is therefore

Choice C

Q5. Two separate wires X and Y have the same original length and cross-sectional area.

The sketch graph above shows the extension ΔL produced in X and Y when the tensile force F applied to the wires is increased up to the point where they break.

Which statement is incorrect?

A
For a given extension more energy is stored in X than in Y.
B
The Young modulus of the material of wire Y is greater than that of wire X.
C
Both wire X and wire Y obey Hooke’s law.
D
Wire X has a greater breaking stress than wire Y.

 

Energy stored is area under the graph - so A is true

E is from the gradient - so B is not true - E for X is greater than Y.

C is true - straight line

D is also true