• Physics 9702 Doubts | Help Page 216

Question 1032: [Matter > Deformation]

The graph shows the relationship between stress and strain for three wires of the same linear dimensions but made from different materials.

Which statements are correct?

1 The extension of P is approximately twice that of Q for the same stress.

2 The ratio of the Young modulus for P to that of Q is approximately two.

3 For strain less than 0.1, R obeys Hooke’s law.

A 1, 2 and 3                B 1 and 3 only                        C 2 and 3 only            D 2 only

Reference: Past Exam Paper – November 2011 Paper 12 Q21

Solution 1032:

Answer: C.

Stress = Force / Area               and Strain = extension / original length

Statement 1: [incorrect]

Consider an equal amount of stress on wire P and Q (draw a horizontal line on the graph). Wire Q has a greater strain than wire P. This means that the extension of wire Q is greater than that of P. The statement is wrong.

It should have been: “The extension of Q is approximately twice that of P for the same stress”.

Statement 2: [correct]

Young modulus E = stress / strain

For the same stress, the strain of Q is approximately twice that of P, thus its Young modulus is half that of P.

Ratio of E_P / E_Q = E / 0.5E = 2

Statement 3: [correct]

Hooke’s law: F = ke

Since stress is proportional to the force and strain is proportional to the extension, it can be concluded that, for Hooke’s law, stress is proportional to strain. In the graph, it is a straight line passing through the origin. So, R obeys Hooke’s law for strain less than 0.1.

Question 1033: [Electromagnetism]

(a) A solenoid is connected in series with a resistor, as shown in Fig. 7.1.

As the magnet is being moved into the solenoid, thermal energy is transferred in the resistor.

Use laws of electromagnetic induction to explain the origin of this thermal energy.

(b) Explain why the alternating current in the primary coil of a transformer is not in phase with the alternating e.m.f. induced in the secondary coil.

Reference: Past Exam Paper – June 2015 Paper 42 Q7

Solution 1033:

(a) The moving magnet gives rise to/causes/induces an e.m.f./current in solenoid/coil. This (induced current) creates a field/flux in the solenoid that opposes the (motion of) magnet. Work is done/energy is needed to move the magnet (into the solenoid). The (induced) current gives heating effect (in resistor) which comes from the work done.

(b) The current in the primary coil give rise to a (magnetic) flux/field. The (magnetic) flux / field (in the core) is in phase with the current (in primary coil). This (magnetic) flux threads/links/cuts the secondary coil inducing an e.m.f. in the secondary coil. The e.m.f. induced is proportional to the rate of change/cutting of flux/field, so it is not in phase {with the alternating current in the primary coil itself}.

Question 1034: [Resistance]

A copper wire is to be replaced by an aluminium alloy wire of the same length and resistance.

Copper has half the resistivity of the alloy.

What is the ratio          diameter of alloy wire / diameter of copper wire ?

A √2                B 2                              C 2√2                          D 4

Reference: Past Exam Paper – June 2014 Paper 12 Q31

Solution 1034:

Answer: A.

Resistance of a wire = ρL / A

Copper wire: Resistance R = ρ_cL / A

Cross-sectional A = ρ_cL / R

Since A proportional to the diameter² (A = πd_c² / 4),

d_c² = 4ρ_cL / R [since we are dealing with a ratio, the π may be eliminated as it is a constant]

Diameter of copper wire, d_c = 2 √(ρ_cL/R)

Aluminium wire: Resistance R = (2ρ_c)L / A

Cross-sectional A = 2ρ_cL / R

d_A² = 8ρ_cL / R

Diameter of aluminium wire, d_A = 2√(2ρ_cL/R) = 2√2 √(ρ_cL/R)

So, ratio = d_A / d_c = √2

Question 1035: [Dynamics > Air resistance]

A body is released from rest and falls vertically in air of constant density.

Which statement about the motion of the falling body is correct?

A As it accelerates, its weight decreases so that its acceleration decreases until it travels with constant velocity.

B It accelerates initially at 9.8 m s^–2 but the drag force increases so its acceleration decreases.

C Its velocity increases at a constant rate until its velocity becomes constant.

D The drag force of the air increases continually and eventually the velocity decreases.

Reference: Past Exam Paper – June 2013 Paper 11 Q7

Solution 1035:

Answer: B.

As the body is released, it falls under the effect of gravity – with an initial acceleration of 9.8 m s^–2.

However, the drag force of the air causes the resultant force on the body to decrease, and thus the acceleration decreases.

The weight of a body is constant in one particular location. [A is incorrect]

‘Velocity increases at a constant rate’ means a constant acceleration, which is incorrect. [C is incorrect]

The drag force increases with an increase in velocity of the body. At one point, the weight would be equal to the drag force and the resultant force on the body becomes zero. From this point, the body no longer accelerates – that is, it travels with a constant velocity. Consequently, the drag force remains constant. [D is incorrect]