Practice gce model questions vol1 physics 2018 Past Questions

Question 1 View Details

A source emits a sound of frequency \(500\ \text{Hz}\). An observer moves directly towards the source at a constant speed of \(20\ \text{m s}^{-1}\) and hears a frequency of \(560\ \text{Hz}\). When the observer then moves directly away from the stationary source at the same speed, the heard frequency is \(440\ \text{Hz}\). Assuming the speed of sound in air is constant, determine the speed of sound \(v\) in the medium (in \(\text{m s}^{-1}\)).

Correct A. 1.67×10^2 m·s⁻¹

B. 1.75×10^2 m·s⁻¹

C. 1.60×10^2 m·s⁻¹

D. 1.55×10^2 m·s⁻¹

Correct Answer: A

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Question 2 View Details

A steel rod of length \(2.00\ \text{m}\) at \(20^{\circ}\text{C}\) expands by \(0.24\ \text{mm}\) when heated to an unknown temperature \(T_1\). When the rod is subsequently cooled from \(T_1\) to \(0^{\circ}\text{C}\) its length decreases by \(0.36\ \text{mm}\) relative to its length at \(T_1\). Assuming the coefficient of linear expansion \(\alpha\) is constant, determine the temperature \(T_1\) (in \(^{\circ}\text{C}\)).

Correct A. 60

B. 75

C. 90

D. 45

Correct Answer: A

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Question 3 View Details

Two thin converging lenses are placed coaxially. Lens 1 has focal length \(f_1 = 10\ \text{cm}\) and Lens 2 has focal length \(f_2 = 20\ \text{cm}\). An object is placed \(30\ \text{cm}\) to the left of Lens 1. The final image formed by the combination is real, inverted and located \(40\ \text{cm}\) to the right of Lens 2. Determine the separation \(d\) (in centimetres) between the two lenses.

Correct A. 55

B. 65

C. 75

D. 45

Correct Answer: A

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Question 4 View Details

A block of mass \(5\ \text{kg}\) is lifted by a compound pulley system. The system consists of a fixed pulley of radius \(0.15\ \text{m}\) and a movable pulley of radius \(0.10\ \text{m}\) attached to the block. A hand‑crank of radius \(0.20\ \text{m}\) is used to rotate the fixed pulley. The coefficient of kinetic friction between the rope and each pulley groove is \(\mu = 0.05\). Assuming the block is raised at constant speed, calculate the minimum constant torque that must be applied to the hand crank (in newton‑metres, to two significant figures).

A. 2.9

B. 5.0

C. 4.2

Correct D. 3.6

Correct Answer: D

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Question 5 View Details

An unknown hydrogen‑like ion X^{2+} emits a photon of wavelength \(73.0\ \text{nm}\) when an electron transitions from the \(n=4\) level to the \(n=2\) level. The ionisation energy of the ion (energy required to remove the electron from the ground state) is measured to be \(122.4\ \text{eV}\). Using the Rydberg formula for hydrogen‑like ions, determine the atomic number \(Z\) of element X and calculate the wavelength (in nanometres, to one decimal place) of the photon emitted when the electron transitions from \(n=5\) to \(n=2\).

Correct A. Z = 3; λ = 54.0 nm

B. Z = 3; λ = 60.0 nm

C. Z = 2; λ = 61.0 nm

D. Z = 4; λ = 48.5 nm

Correct Answer: A

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Question 6 View Details

A vertical rectangular gate 2.0 m wide and 1.5 m high is hinged at its top edge and is completely submerged in fresh water. The top edge of the gate is 2.0 m below the water surface. Determine (a) the magnitude of the total hydrostatic force on the gate, and (b) the depth of the centre of pressure measured from the water surface. Take \(\rho = 1000\ \text{kg\,m}^{-3}\) and \(g = 9.8\ \text{m\,s}^{-2}\).

A. Force = 9.12×10⁴ N, centre of pressure depth = 2.82 m

B. Force = 7.35×10⁴ N, centre of pressure depth = 2.55 m

Correct C. Force = 8.09×10⁴ N, centre of pressure depth = 2.82 m

D. Force = 8.09×10⁴ N, centre of pressure depth = 3.10 m

Correct Answer: C

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Question 7 View Details

A particle moves 5.0 m east and then 12.0 m north. Find the magnitude of the resultant displacement and state its direction measured north of east.

Correct A. 13.0 m, 67.4° north of east

B. 13.0 m, 45.0° north of east

C. 12.0 m, 67.4° north of east

D. 13.0 m, 72.5° north of east

Correct Answer: A

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Question 8 View Details

A source emits sound of frequency \(f = 500\ \text{Hz}\) in air where the speed of sound is \(v = 340\ \text{m\,s}^{-1}\). The source moves directly towards a stationary observer at \(30\ \text{m\,s}^{-1}\). At the same time the observer moves directly away from the source at \(20\ \text{m\,s}^{-1}\) along the same line. Calculate the frequency heard by the observer.

Correct A. 516 Hz (approximately)

B. 500 Hz (approximately)

C. 530 Hz (approximately)

D. 540 Hz (approximately)

Correct Answer: A

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Question 9 View Details

A string of length \(L = 0.80\ \text{m}\) is fixed at both ends. Its linear mass density is \(\mu = 0.010\ \text{kg\,m}^{-1}\) and it is under a tension of \(T = 100\ \text{N}\). Determine the frequency of the third harmonic (n = 3) of the standing wave on the string.

A. 180 Hz

Correct B. 187.5 Hz

C. 150 Hz

D. 200 Hz

Correct Answer: B

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Question 10 View Details

The diagram shows a smooth inclined plane making an angle of \(30^{\circ}\) with the horizontal and having a length of \(5.0\ \text{m}\). A block of mass \(2.0\ \text{kg}\) starts from rest at the top and slides down without friction. At the bottom it compresses a horizontal spring of spring constant \(k = 800\ \text{N\,m}^{-1}\) until the block momentarily comes to rest. Assuming mechanical energy is conserved, calculate the maximum compression of the spring.

A. 0.55 m

Correct B. 0.35 m

C. 0.45 m

D. 0.30 m

Correct Answer: B

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Question 11 View Details

The diagram shows three forces acting on a particle. Force A has magnitude \(10\) N acting horizontally to the right. Force B has magnitude \(8\) N acting at \(150^{\circ}\) measured anticlockwise from the positive x‑axis. Force C acts at \(232.5^{\circ}\) (measured anticlockwise from the positive x‑axis) and its magnitude is unknown. The particle is in equilibrium. Find the magnitude of Force C (in newtons, correct to two significant figures).

A. 7.8

B. 4.1

Correct C. 5.0

D. 6.3

Correct Answer: C

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Question 12 View Details

A 200 g piece of aluminium (specific heat \(c_{Al}=0.900\) kJ kg\(^{-1}\) K\(^{-1}\)) at \(150^{\circ}\)C is placed into 500 g of water (specific heat \(c_{w}=4.18\) kJ kg\(^{-1}\) K\(^{-1}\)) initially at \(20^{\circ}\)C in an insulated container. After the system reaches equilibrium its temperature is \(T_{1}\). The mixture is then transferred into a calorimeter whose initial temperature is \(20^{\circ}\)C and whose heat capacity \(C_{cal}\) (in kJ K\(^{-1}\)) is unknown. After the transfer the final temperature of the whole system is \(30^{\circ}\)C. Determine the heat capacity \(C_{cal}\) of the calorimeter (express your answer in kJ K\(^{-1}\) to two significant figures).

A. 0.050

Correct B. 0.070

C. 0.120

D. 0.090

Correct Answer: B

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Question 13 View Details

A battery of unknown emf \(E\) V and internal resistance \(r\) \(\Omega\) is connected to a variable external resistor \(R\). When \(R=6\) \(\Omega\) the terminal voltage measured across the external resistor is \(9\) V. When \(R=3\) \(\Omega\) the terminal voltage is \(8\) V. Determine the emf \(E\) of the battery (to two significant figures) and its internal resistance \(r\) (to two significant figures).

A. E = 11 V, r = 0.5 Ω

Correct B. E = 10 V, r = 0.86 Ω

C. E = 9.5 V, r = 1.0 Ω

D. E = 12 V, r = 0.75 Ω

Correct Answer: B

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Question 14 View Details

A block of mass \(5\) kg rests on a rough inclined plane that makes an angle of \(30^{\circ}\) with the horizontal. A constant horizontal force of \(60\) N is applied to the block (the force acts horizontally, not along the plane). The coefficient of kinetic friction between the block and the plane is \(\mu_k = 0.20\). Assuming the block moves up the plane, calculate the magnitude of its acceleration (in \(\text{m s}^{-2}\), to two significant figures).

A. 2.0

Correct B. 2.6

C. 1.9

D. 3.1

Correct Answer: B

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Question 15 View Details

State whether each of the following quantities is a scalar or a vector: (i) displacement, (ii) speed, (iii) force, (iv) mass.

Correct A. displacement: vector; speed: scalar; force: vector; mass: scalar

B. displacement: vector; speed: scalar; force: scalar; mass: vector

C. displacement: vector; speed: vector; force: vector; mass: scalar

D. displacement: scalar; speed: vector; force: vector; mass: scalar

Correct Answer: A

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Question 16 View Details

A long solenoid of length \(0.50\ \text{m}\) and radius \(0.04\ \text{m}\) has \(800\) turns and carries a current \(I\). It is placed in a uniform external magnetic field of magnitude \(1.2\times10^{-3}\ \text{T}\) directed parallel to the solenoid axis. (a) Determine the current required so that the magnetic field at the centre of the solenoid is exactly twice the external field. (b) A small magnetic dipole with moment \(\mu =5.0\times10^{-3}\ \text{A·m}^2\) is placed at the centre, initially making an angle of \(30^{\circ}\) with the combined field direction. Calculate the magnitude of the torque acting on the dipole. (c) Assuming the dipole can rotate freely about the axis, find its angular acceleration if its moment of inertia about that axis is \(2.0\times10^{-4}\ \text{kg·m}^2\).

Correct A. I = 0.60 A, \tau = 6.0\times10^{-6} N·m, \alpha = 3.0\times10^{-2} rad·s^{-2}

B. I = 0.60 A, \tau = 5.0\times10^{-6} N·m, \alpha = 2.0\times10^{-2} rad·s^{-2}

C. I = 0.45 A, \tau = 4.5\times10^{-6} N·m, \alpha = 2.5\times10^{-2} rad·s^{-2}

D. I = 0.75 A, \tau = 7.2\times10^{-6} N·m, \alpha = 3.6\times10^{-2} rad·s^{-2}

Correct Answer: A

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Question 17 View Details

A resistor has a resistance of \(6.0\ \Omega\) at \(20^{\circ}\text{C}\) and a temperature coefficient of resistance \(\alpha =2.0\times10^{-3}\ \text{°C}^{-1}\). It is connected in series with a battery of emf \(E\) and internal resistance \(r\). When the resistor is at \(20^{\circ}\text{C}\) the current measured is \(2.00\ \text{A}\). When the resistor is uniformly heated to \(50^{\circ}\text{C}\) the current falls to \(1.90\ \text{A}\). Determine (a) the internal resistance \(r\) of the battery and (b) the emf \(E\) of the battery.

A. r = 1.00 \Omega, \; E = 14.20 V

Correct B. r = 0.84 \Omega, \; E = 13.68 V

C. r = 0.84 \Omega, \; E = 12.00 V

D. r = 0.70 \Omega, \; E = 12.50 V

Correct Answer: B

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Question 18 View Details

A particle moves along a straight line with a time‑dependent acceleration given by \(a(t)=k\,t\), where \(k\) is a constant. At \(t=0\) its speed is \(3.0\ \text{m s}^{-1}\). After \(4.0\ \text{s}\) it has travelled a distance of \(50\ \text{m}\). (a) Find the value of \(k\). (b) Determine its speed at \(t=4.0\ \text{s}\). (c) Calculate the additional distance it travels between \(t=4.0\ \text{s}\) and \(t=6.0\ \text{s}\).

A. k = 2.80 m·s^{-3}, \; v(4\,\text{s}) = 28.0 m·s^{-1}, \; \Delta s = 85.0 m

B. k = 4.10 m·s^{-3}, \; v(4\,\text{s}) = 34.2 m·s^{-1}, \; \Delta s = 105.5 m

C. k = 3.00 m·s^{-3}, \; v(4\,\text{s}) = 30.0 m·s^{-1}, \; \Delta s = 90.0 m

Correct D. k = 3.56 m·s^{-3}, \; v(4\,\text{s}) = 31.5 m·s^{-1}, \; \Delta s = 96.3 m

Correct Answer: D

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Question 19 View Details

A block of mass \(2.0\ \text{kg}\) starts from rest at the top of a rough inclined plane that is \(5.0\ \text{m}\) long and makes an angle of \(30^{\circ}\) with the horizontal. The coefficient of kinetic friction between the block and the plane is \(\mu_{k}=0.15\). (a) Find the speed of the block when it reaches the bottom. (b) Determine the time taken to travel down the plane. (c) Compute the instantaneous power dissipated by friction at the instant the block reaches the bottom.

A. v = 5.80 m·s^{-1}, \; t = 1.70 s, \; P_{fric} = 14.5 W

B. v = 5.50 m·s^{-1}, \; t = 1.80 s, \; P_{fric} = 13.0 W

C. v = 6.50 m·s^{-1}, \; t = 1.50 s, \; P_{fric} = 17.0 W

Correct D. v = 6.02 m·s^{-1}, \; t = 1.66 s, \; P_{fric} = 15.3 W

Correct Answer: D

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Question 20 View Details

A block‑and‑tackle arrangement consists of one fixed pulley and one movable pulley, giving an ideal mechanical advantage of 2. It is used to lift a load of \(200\ \text{N}\). The system is operated at constant speed and has an overall mechanical efficiency of \(80\%\). (a) What is the tension in the rope? (b) What is the magnitude of the force that must be applied by the person pulling the rope? (c) How far must the rope be pulled to raise the load through a vertical distance of \(0.50\ \text{m}\)?

Correct A. T = 125 N, \; F_{pull} = 125 N, \; d_{pull} = 1.00 m

B. T = 100 N, \\; F_{pull} = 100 N, \\; d_{pull} = 1.00 m

C. T = 125 N, \\; F_{pull} = 156 N, \\; d_{pull} = 1.25 m

D. T = 150 N, \\; F_{pull} = 150 N, \\; d_{pull} = 0.80 m

Correct Answer: A

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Question 21 View Details

A car starts from rest and accelerates uniformly. After travelling a distance of \(100\ \text{m}\) its speed is \(20\ \text{m\,s}^{-1}\). Determine the magnitude of its acceleration and the time taken to travel the \(100\ \text{m}\).

A. a = 2.0 \\ \\text{m\\,s}^{-2}, \\; t = 9 \\ \\text{s}

B. a = 2.5 \\ \\text{m\\,s}^{-2}, \\; t = 8 \\ \\text{s}

C. a = 1.5 \\ \\text{m\\,s}^{-2}, \\; t = 12 \\ \\text{s}

Correct D. a = 2.0 \ \text{m\,s}^{-2}, \; t = 10 \ \text{s}

Correct Answer: D

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Question 22 View Details

A rectangular conducting loop of width \(w = 0.15\ \text{m}\) and length \(l = 0.30\ \text{m}\) and resistance \(R = 5\ \Omega\) is pulled out of a uniform magnetic field \(B = 0.8\ \text{T}\). The loop starts from rest and moves with constant acceleration, leaving the field completely after \(4.0\ \text{s}\).\n\n(a) Find the magnitude of the acceleration.\n\n(b) Determine the induced emf at the instant when exactly half of the loop is still within the field.\n\n(c) Calculate the total energy dissipated as heat in the loop during the whole motion.

A. a = 2.0\times10^{-2}\\ \text{m\\,s}^{-2}, \\; \\varepsilon_{half}=1.5\times10^{-2}\\ \text{V}, \\; E_{heat}=9.5\times10^{-5}\\ \text{J}

Correct B. a = 1.88\times10^{-2}\ \text{m\,s}^{-2}, \; \varepsilon_{half}=1.27\times10^{-2}\ \text{V}, \; E_{heat}=8.6\times10^{-5}\ \text{J}

C. a = 2.5\times10^{-2}\\ \text{m\\,s}^{-2}, \\; \\varepsilon_{half}=1.0\times10^{-2}\\ \text{V}, \\; E_{heat}=1.2\times10^{-4}\\ \text{J}

D. a = 1.5\times10^{-2}\\ \text{m\\,s}^{-2}, \\; \\varepsilon_{half}=1.5\times10^{-2}\\ \text{V}, \\; E_{heat}=7.0\times10^{-5}\\ \text{J}

Correct Answer: B

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Question 23 View Details

A block of mass \(5.0\ \text{kg}\) rests on a rough inclined plane that makes an angle of \(30^{\circ}\) with the horizontal. The coefficients of static and kinetic friction are \(\mu_{s}=0.40\) and \(\mu_{k}=0.30\) respectively. A horizontal force \(F\) is applied to the block.\n\n(i) Determine the minimum magnitude of \(F\) required to start the block moving up the incline.\n\n(ii) If the applied horizontal force is increased to \(70\ \text{N}\), find the acceleration of the block up the plane once it is in motion.

A. F_{min} \approx 6.2\times10^{1}\ \text{N}, \; a \approx 1.8\ \text{m\,s}^{-2} (for F=70\ \text{N})

Correct B. F_{min} \approx 6.2\times10^{1}\ \text{N}, \; a \approx 2.6\ \text{m\,s}^{-2} (for F=70\ \text{N})

C. F_{min} \approx 7.0\times10^{1}\ \text{N}, \; a \approx 2.0\ \text{m\,s}^{-2} (for F=70\ \text{N})

D. F_{min} \approx 5.4\times10^{1}\ \text{N}, \; a \approx 3.0\ \text{m\,s}^{-2} (for F=70\ \text{N})

Correct Answer: B

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Question 24 View Details

Three point charges are placed at the vertices of a right‑angled triangle \(ABC\) with \(\angle ABC = 90^{\circ}\). The sides are \(AB = 0.20\ \text{m}\), \(BC = 0.15\ \text{m}\) and \(AC\) is the hypotenuse. The charges are \(q_{1}=+5\ \mu\text{C}\) at \(A\), \(q_{2}=-3\ \mu\text{C}\) at \(B\) and \(q_{3}=+2\ \mu\text{C}\) at \(C\).\n\n(a) Find the magnitude and direction of the net electric field at the midpoint \(M\) of side \(AC\).\n\n(b) A test charge \(q_{t}=+1\ \mu\text{C}\) is moved quasistatically from \(M\) to the midpoint \(D\) of side \(BC\). Calculate the work done by the external agent in this process.\n\n(c) The whole configuration is rotated through \(180^{\circ}\) about the midpoint of \(BC\). How does the magnitude of the electric field at the new position of \(M\) compare with that found in part (a)?

A. |E| = 3.10\times10^{6}\ \text{N\,C}^{-1} \text{ (upward)}, \; W = 0.20\ \text{J}, \; the magnitude after rotation is increased (3.10\times10^{6}\ \text{N\,C}^{-1})

B. |E| = 2.50\times10^{6}\ \text{N\,C}^{-1} \text{ (downward)}, \; W = -0.15\ \text{J}, \; the magnitude after rotation is unchanged (2.50\times10^{6}\ \text{N\,C}^{-1})

Correct C. |E| = 2.76\times10^{6}\ \text{N\,C}^{-1} \text{ (downward)}, \; W = -0.20\ \text{J}, \; the magnitude after rotation is unchanged (2.76\times10^{6}\ \text{N\,C}^{-1})

D. |E| = 2.76\times10^{6}\ \text{N\,C}^{-1} \text{ (downward)}, \; W = -0.20\ \text{J}, \; the magnitude after rotation is halved (1.38\times10^{6}\ \text{N\,C}^{-1})

Correct Answer: C

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Question 25 View Details

A displacement vector \(\vec A\) of magnitude \(5.0\ \text{m}\) is directed \(30^{\circ}\) north of east. A second displacement vector \(\vec B\) of magnitude \(8.0\ \text{m}\) is directed \(45^{\circ}\) south of east.\n\n(i) Determine the magnitude of the resultant displacement \(\vec R = \vec A + \vec B\).\n\n(ii) State whether the resultant displacement is a scalar or a vector quantity.

Correct A. |R| \approx 10.5\ \text{m}; \; \text{vector}

B. |R| \approx 9.2\ \text{m}; \; \text{vector}

C. |R| \approx 7.5\ \text{m}; \; \text{vector}

D. |R| \approx 12.0\ \text{m}; \; \text{vector}

Correct Answer: A

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