• Physics 9702 Doubts | Help Page 53

Question 309: [Forces > Hooke’s law]
A uniform strip of rubber, marked with equal divisions, is fixed at end P and pulled into tension by a force F applied at end Q, as shown in the diagram below.

Which one of the following diagrams correctly shows the separation of the division when the elastic is extended to twice its original length?

Reference: Past Exam Paper – N86 / I / 30



Solution 309:
Answer: C.
Rubber behaves elastically – it regains its original shape when a deforming force is removed.
Rubber is a polymer. It consists of very long chain molecules. The chains of molecules are all tangled up.  When a piece of rubber is stretched, the chains of molecules are pulled in the direction of strain; the chains of molecules are straightened. Because of this, a piece of rubber can be stretched to approximately 3 times its original length before breaking compared to a breaking strain of about 1% for steel.

{Breaking strain is the value of strain at which the material breaks.}

Since the strip of rubber is uniform and marked with equal divisions, when it is extended to twice its original length, the markings will still be separated equally, with the separation being twice that on the rubber before the force is applied.









Question 310: [Measurements > Uncertainty]
Student uses a digital ammeter to measure a current. Reading of the ammeter is found to fluctuate between 1.98A and 2.02A. Manufacturer of the ammeter states that any reading has a systematic uncertainty of ±1%. Which value of current should be quoted by the student?
A (2.00 ± 0.01) A
B (2.00 ± 0.02) A
C (2.00 ± 0.03) A
D (2.00 ± 0.04) A

Reference: Past Exam Paper – November 2008 Paper 1 Q4



Solution 310:

Answer: D.

Mean value of current = (1.98 + 2.02) /2 = 2.00 A

Random uncertainty in value of current = ± 0.02 A
{Random uncertainty is the uncertainty due to random errors.}

Any value has a systematic uncertainty of ± 1%

1% of 2.00 A = 2.00 / 100 = 0.02 A

Systematic uncertainty in value of current = ± 0.02 A

Total uncertainty in value of current = ± (0.02 + 0.02) = ± 0.04 A

So, the value of current should be quoted as (2.00 ± 0.04) A

Question 311: [Physics of Materials ~ Matter > Solids]
The diagram below represents the extension-load curves for three specimens X, Y and Z, which were of the same unextended dimensions.

Which of the following combinations could indicate the materials from which the specimens were made?

Reference: Past Exam Paper – J86 / I / 30



Solution 311:
Answer: A.
The 3 materials suggested in the choices are glass, copper and rubber.

Glass is an amorphous solid. It does not show plastic behavior (it does not undergo plastic deformation), but it is brittle – that is, it breaks when some amount of force is applied to it.  So, specimen X could be X – it does not undergo much extension.

Copper is a metal (a crystalline solid). It can be extended elastically by some amount of forces until it reaches the elastic limit. Beyond the elastic limit, it undergoes plastic deformation. This would correspond to specimen Y.

Rubber is a polymer. It consists of very long chain molecules. The chains of molecules are all tangled up.  When a piece of rubber is stretched, the chains of molecules are pulled in the direction of strain; the chains of molecules are straightened. Because of this, a piece of rubber can be stretched to approximately 3 times its original length before breaking compared to a breaking strain of about 1% for steel.
So, rubber can undergo a much larger extension than a metal for the same force applied. Rubber corresponds to specimen Z.


Rubber departs from Hooke’s law, but it behaves elastically. It can be extended much more than metals (which obey Hooke’s law up to the limit of proportionality). [In this question, from the materials suggested, rubber is more likely to be specimen Z.]
 








Question 312: [Measurements > Estimates]
What is a reasonable estimate of diameter of an alpha particle?
A 10^–15m                     B 10^–12 m                     C 10^–9 m                      D 10^–6 m

Reference: Past Exam Paper – November 2007 Paper 1 Q2



Solution 312:

Answer: A.

These types of questions are not based on guesswork. Some benchmarks for physical quantities is really useful.

For example, ‘an atom has a diameter around 10^-10 m’

An alpha particle is the nucleus of a Helium atom.

A nucleus has a diameter only about 1/100 000 that of an atom.

Question 313: [Forces > Hooke’s law]
A spring obeying Hooke’s law has unstretched length of 50mm and a spring constant of 400Nm^-1.
What is the tension in the spring when its overall length is 70mm?
A 8.0 N                       B 28 N                        C 160 N                      D 400 N

Reference: Past Exam Paper – N94 / I / 23



Solution 313:
Answer: A
Hooke’s law: F = kx

Extension, x = 70 – 50 = 20mm = 0.02m

Tension, F = kx = 400 (0.02) = 8.0 N