• Physics 9702 Doubts | Help Page 93

Question 478: [Matter > Elasticity]

Energy is stored in metal wire that is extended elastically.

(a) Explain what is meant by extended elastically.

(b) Show that SІ units of energy per unit volume are kg m^–1 s^–2.

(c) For a wire extended elastically, elastic energy per unit volume X is given by

X = Cε²E

where C is a constant, ε is strain of the wire, and E is Young modulus of the wire.

Show that C has no units.

Reference: Past Exam Paper – June 2013 Paper 21 Q1

Solution 478:

(a) The wire returns to its original length (not ‘shape’) when the load is removed

(b)

Units of energy: Nm or kg m² s^-2

Units of volume: m³

Unit of energy / volume: kg m² s^-2 / m³ = kg m^-1 s^-2

(c)

Strain (= extension / original length) ε of the wire has no units

{Young modulus E = stress / strain. Stress = Force / Area}

Units of Young modulus E: kg ms^-2 m^-2 = kg m^-1 s^-2

The units of the right-hand side terms is the same as the units of the left-hand side terms. So, C has no units.

Question 479: [Work, Energy, Power]

In many old-style filament lamps, as much as 92 J of energy is emitted as thermal energy for every 8 J of energy emitted as light.

What is efficiency of the lamp, as the percentage of electrical energy converted to light energy?

A 8 %                         B 9 %                         C 91 %                                    D 92 %

Reference: Past Exam Paper – November 2011 Paper 12 Q17

Solution 479:

Answer: A.

Useful output energy (emitted as light) = 8J

Wasted energy (emitted as thermal energy) = 92J

Total energy output = 92 + 8 = 100J

Efficiency = useful output energy / total output energy = 8 / 100 = 8%

Question 480: [Waves > Interference]

Coherent waves are produced at P and at Q and travel outwards in all directions. Line RS is halfway between P and Q and perpendicular to the line joining P and Q. Distance RS is much greater than the distance PQ.

Along which line, or lines, is interference pattern observed?

A both RS and XY

B RS only

C XY only

D neither RS nor XY

Reference: Past Exam Paper – November 2011 Paper 11 Q30 & Paper 13 Q29

Solution 480:

Answer: C.

An interference pattern consists of a series of alternating constructive interference (bright spot for light waves) and destructive interference (dark spot for light waves). An interference pattern will not be observed along a line where only constructive or destructive interference occur.

Interference pattern is only observed along line XY.

Note that the waves are produced at P and Q. The phase difference between the waves from P and Q is constant along line RS (since waves are coherent and RS is midway from P and Q). Thus, the path difference along RS is always zero – that is, only constructive interference occur along this line (for constructive interference, path difference = nλ where n = 0, 1, 2, 3, …). So, there can be no interference pattern along RS.

Question 481: [Waves > Interference]

Two identical loudspeakers are connected in series to a.c. supply, as shown.

Which graph best shows variation of the intensity of the sound with distance along the line XY?

Reference: Past Exam Paper – November 2014 Paper 11 & 12 Q26

Solution 481:

Answer: D.

For point sources, an interference pattern of alternating constructive and destructive interference would be observed along XY. However, loudspeakers are NOT point sources of sound. So, there will be no place where the sound intensity is exactly zero. [B and C are incorrect]

The intensity of the maxima is the highest at the centre on line XY, midway between the 2 loudspeakers and the maxima gradually decrease in intensity away from the central maximum because the individual amplitudes of the two sound waves decrease with distance. The intensity of waves is inversely proportional to the square of the distance apart. [A is incorrect]

The interference pattern is represented by the rise and fall of the intensity.

Question 482: [Measurements]

A micrometer screw gauge is used to measure diameter of a copper wire.

Reading with the wire in position is shown in diagram 1. Wire is removed and the jaws of the micrometer are closed. New reading is shown in diagram 2.

What is the diameter of wire?

A 1.90 mm                  B 2.45 mm                  C 2.59 mm                  D 2.73 mm

Reference: Past Exam Paper – June 2010 Paper 12 Q1

Solution 482:

Answer: B.

When the wire is removed, the reading is 0.14mm (as shown in diagram 2) instead of being zero. This means that there is a zero error in the micrometer. When the jaws are closed, instead of giving a reading of zero, the reading already has a value of 0.14mm. So, any measurement taken is greater by a value of 0.14mm.

Reading when the wire is measured = 2.59mm

So, diameter of wire = 2.59 – 0.14 = 2.45mm