Practice gce model questions vol1 physics 2017 Past Questions

Question 1 View Details

A car starts from rest and moves with uniform acceleration. In the first \(5\ \text{s}\) it travels \(100\ \text{m}\). Determine the magnitude of the acceleration and the speed of the car at \(t = 5\ \text{s}\).

A. acceleration = 6.4 m\/s^2, speed = 32 m\/s

B. acceleration = 5 m\/s^2, speed = 25 m\/s

C. acceleration = 10 m\/s^2, speed = 50 m\/s

Correct D. acceleration = 8 m/s^2, speed = 40 m/s

Correct Answer: D

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Question 2 View Details

A 200 g iron block at \(150^{\circ}\text{C}\) is placed into 500 g of water at \(20^{\circ}\text{C}\) in an insulated container. After equilibrium the water temperature is measured to be \(30^{\circ}\text{C}\). Assuming no heat is lost to the surroundings, the heat lost by the iron should equal the heat gained by the water. Using the specific heats \(c_{\text{Fe}} = 0.45\ \text{J g}^{-1}\!^{\circ}\text{C}^{-1}\) and \(c_{\text{H}_2\text{O}} = 4.18\ \text{J g}^{-1}\!^{\circ}\text{C}^{-1}\), calculate the amount of heat (in joules) that must have been supplied to the system from the surroundings.

A. 8600 J

Correct B. 10100 J

C. 11200 J

D. 9500 J

Correct Answer: B

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Question 3 View Details

An object 2.0 cm tall is placed \(30\ \text{cm}\) to the left of a converging lens L\(_1\) of focal length \(12\ \text{cm}\). A second converging lens L\(_2\) of focal length \(8\ \text{cm}\) is positioned \(10\ \text{cm}\) to the right of L\(_1\). Determine (i) the position of the final image relative to L\(_2\) and (ii) the overall linear magnification of the system.

Correct A. final image 1.21 cm to the right of L2; overall magnification ≈0.24 (image height ≈0.48 cm)

B. final image 2.10 cm to the right of L2; overall magnification ≈0.31 (image height ≈0.62 cm)

C. final image 0.85 cm to the right of L2; overall magnification ≈0.18 (image height ≈0.36 cm)

D. final image 1.80 cm to the left of L2; overall magnification ≈0.27 (image height ≈0.54 cm)

Correct Answer: A

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Question 4 View Details

A source of sound emits a frequency \(f_0 = 500\ \text{Hz}\) and moves towards a stationary observer with speed \(30\ \text{m s}^{-1}\). The speed of sound in air is \(340\ \text{m s}^{-1}\). A rigid wall is located \(100\ \text{m}\) behind the source. The observer receives both the direct sound and the sound reflected from the wall. Calculate the frequency of the reflected sound heard by the observer.

A. 500 Hz

Correct B. 460 Hz

C. 470 Hz

D. 440 Hz

Correct Answer: B

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Question 5 View Details

The motion diagram shows a particle at three successive times: at \(t = 0\ \text{s}\) the particle is at \(x = 0\ \text{m}\); at \(t = 2\ \text{s}\) it is at \(x = 8\ \text{m}\); and at \(t = 4\ \text{s}\) it is at \(x = 32\ \text{m}\). Assuming the particle moves with constant acceleration, determine the magnitude of the acceleration.

A. 6 m/s^2

B. 8 m/s^2

Correct C. 4 m/s^2

D. 2 m/s^2

Correct Answer: C

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Question 6 View Details

A rectangular coil of N = 200 turns and area A = 0.020\,m^{2} rotates uniformly in a uniform magnetic field of magnitude B = 0.5\,T. The coil has an internal resistance of 5\,\Omega and is connected to an external resistor. The peak induced emf in the coil is given by \(\varepsilon = N B A \omega\), where \(\omega\) is the angular speed in rad\,s^{-1}.\n\n(i) Determine the angular speed \(\omega\) (to two decimal places) required so that, when the external resistor is chosen to maximise the instantaneous power transferred to it, the maximum power is 2.0\,W.\n\n(ii) If the coil is then rotated at half this angular speed, what is the greatest instantaneous power that can be delivered to any external resistor? Give your answer to two decimal places in watts.

A. ω = 3.50 rad s⁻¹; maximum power at half speed = 0.55 W

B. ω = 2.83 rad s⁻¹; maximum power at half speed = 0.45 W

C. ω = 3.16 rad s⁻¹; maximum power at half speed = 0.60 W

Correct D. ω = 3.16 rad s⁻¹; maximum power at half speed = 0.50 W

Correct Answer: D

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Question 7 View Details

A composite rod consists of two sections in series. Section A is copper (thermal conductivity \(k_{1}=400\,\text{W\,m}^{-1}\text{K}^{-1}\)), length \(L_{1}=0.50\,\text{m}\) and cross‑sectional area \(A_{1}=1.0\times10^{-4}\,\text{m}^{2}\). Section B is steel (\(k_{2}=50\,\text{W\,m}^{-1}\text{K}^{-1}\)), length \(L_{2}=0.30\,\text{m}\) and area \(A_{2}=2.0\times10^{-4}\,\text{m}^{2}\). The end of the copper section is maintained at \(120^{\circ}\text{C}\) and the opposite end of the steel section is kept at \(20^{\circ}\text{C}\). Assuming steady‑state heat flow, find the temperature at the junction between the two sections (to one decimal place in °C).

Correct A. 90.6 °C

B. 85.2 °C

C. 80.0 °C

D. 95.4 °C

Correct Answer: A

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Question 8 View Details

A police car equipped with a siren of frequency \(f = 800\,\text{Hz}\) moves directly towards a stationary observer. The temperature of the air is \(25^{\circ}\text{C}\). The observer measures the frequency of the siren as \(880\,\text{Hz}\).\n\n(i) Calculate the speed of the police car (in m\,s^{-1}, to one decimal place).\n\n(ii) If the air temperature rises to \(35^{\circ}\text{C}\) while the car continues at the same speed, what frequency will the observer now hear? Give your answer to one decimal place in hertz.

A. Speed = 33.2 m\/s; new observed frequency = 876.0 Hz

B. Speed = 28.0 m\/s; new observed frequency = 882.0 Hz

C. Speed = 30.0 m\/s; new observed frequency = 880.0 Hz

Correct D. Speed = 31.5 m/s; new observed frequency = 878.5 Hz

Correct Answer: D

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Question 9 View Details

A \(1.00\,\text{g}\) sample of the radioactive isotope \(^{238}\text{U}\) (half‑life \(T_{A}=4.5\times10^{9}\,\text{yr}\)) decays to \(^{234}\text{Th}\), which in turn decays to a stable nuclide with half‑life \(T_{B}=1.0\times10^{5}\,\text{yr}\). Initially the sample contains only \(^{238}\text{U}\). After a period of \(2.0\times10^{5}\,\text{yr}\):\n\n(i) What is the activity of the daughter nuclide \(^{234}\text{Th}\) (in becquerels, to two significant figures)?\n\n(ii) What fraction of the original \(^{238}\text{U}\) atoms have decayed by that time? Express your answer in scientific notation to two significant figures.

A. Activity = 8.5×10^3 Bq; fraction decayed = 2.8×10⁻⁵

Correct B. Activity = 9.3×10^3 Bq; fraction decayed = 3.1×10⁻⁵

C. Activity = 1.0×10^4 Bq; fraction decayed = 3.5×10⁻⁵

D. Activity = 9.3×10^2 Bq; fraction decayed = 3.1×10⁻⁴

Correct Answer: B

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Question 10 View Details

Three point charges are placed at the vertices of an equilateral triangle of side \(a = 0.10\,\text{m}\). The charges are \(q_{A}=+2\,\mu\text{C}\) at vertex A, \(q_{B}=-3\,\mu\text{C}\) at vertex B and \(q_{C}=+5\,\mu\text{C}\) at vertex C. The triangle lies in vacuum.\n\n(i) Determine the magnitude of the resultant electric field at the centre O of the triangle (in N\,C^{-1}, to two significant figures) and state its direction as an angle measured clockwise from the positive x‑axis.\n\n(ii) A test charge of \(+1\,\mu\text{C}\) is brought from infinity to the centre O. Calculate the work done on the test charge (in joules, to two significant figures).

Correct A. E = 1.9×10^7 N/C at 188° clockwise from +x; work = 0.62 J

B. E = 1.7×10^7 N/C at 188° clockwise from +x; work = 0.70 J

C. E = 1.9×10^7 N/C at 210° clockwise from +x; work = 0.62 J

D. E = 2.1×10^7 N/C at 172° clockwise from +x; work = 0.55 J

Correct Answer: A

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Question 11 View Details

A metal rod is \(2.5\ \text{m}\) long at 20\,\degree C. When its temperature is raised, it expands by \(0.12\%\) of its original length. Find the new length of the rod in centimetres.

A. 251.2 cm

B. 250.6 cm

Correct C. 250.3 cm

D. 250.0 cm

Correct Answer: C

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Question 12 View Details

A battery has an unknown emf \(E\) and internal resistance \(r\). When a single lamp of resistance \(R\) is connected across its terminals, a current of \(2.0\ \text{A}\) flows and the terminal voltage is \(8.0\ \text{V}\). When a second identical lamp is connected in parallel with the first, the total current supplied by the battery becomes \(3.0\ \text{A}\). Determine (i) the emf \(E\) of the battery, (ii) the internal resistance \(r\), and (iii) the efficiency (useful power delivered to the two lamps divided by the total power output of the battery) for the parallel arrangement. Express the efficiency as a percentage.

A. E = 12 V, r = 1 Ω, efficiency = 55%

Correct B. E = 12 V, r = 2 Ω, efficiency = 50%

C. E = 14 V, r = 2 Ω, efficiency = 40%

D. E = 10 V, r = 2 Ω, efficiency = 45%

Correct Answer: B

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Question 13 View Details

A particle moves in a straight line. It starts from rest, accelerates uniformly at \(2.0\ \text{m s}^{-2}\) for a time \(t_{1}\), then travels at the attained constant speed for a time \(t_{2}\), and finally decelerates uniformly at \(3.0\ \text{m s}^{-2}\) to come to rest in a time \(t_{3}\). The total distance covered is \(500\ \text{m}\) and the total time taken is \(40\ \text{s}\). Find the distance travelled during the constant‑speed portion of the motion.

A. 425 m

B. 382 m

Correct C. 409 m

D. 367 m

Correct Answer: C

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Question 14 View Details

A pipe that is open at one end and closed at the other has a length of \(1.20\ \text{m}\). When a tuning fork of frequency \(210\ \text{Hz}\) is held near the open end, a standing wave is produced. Assuming the speed of sound in air is \(340\ \text{m s}^{-1}\), determine the next higher frequency at which a standing wave can be produced in the same pipe, and give the wavelength of that mode.

Correct A. 354 Hz, 0.96 m

B. 420 Hz, 0.81 m

C. 210 Hz, 1.62 m

D. 300 Hz, 1.13 m

Correct Answer: A

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Question 15 View Details

A U‑tube manometer contains water (\(\rho_{\text{w}} = 1000\ \text{kg m}^{-3}\)). Mercury (\(\rho_{\text{Hg}} = 13600\ \text{kg m}^{-3}\)) is poured into the right arm, forming a column \(0.12\ \text{m}\) high above the water level in that arm. The water levels in the two arms differ by \(0.30\ \text{m}\), the water in the left arm being higher. The right arm is open to the atmosphere. Find the gauge pressure of the gas in the left arm (i.e., the pressure above atmospheric pressure) in pascals.

A. 1.48e4 Pa

B. 9.8e3 Pa

Correct C. 1.31e4 Pa

D. 1.05e4 Pa

Correct Answer: C

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Question 16 View Details

A \(5.0\ \text{kg}\) block is pulled up a \(30^{\circ}\) incline of length \(8.0\ \text{m}\) by a constant horizontal force of \(60\ \text{N}\). The coefficient of kinetic friction between the block and the incline is \(\mu_k = 0.20\). The block starts from rest at the bottom. (a) Find the speed of the block when it reaches the top of the incline. (b) Find the average power delivered by the horizontal force during the motion.

A. Speed \(=5.12\ \text{m s}^{-1}\); average power \(=1.20\times10^{2}\ \text{W}\)

B. Speed \(=6.00\ \text{m s}^{-1}\); average power \(=1.50\times10^{2}\ \text{W}\)

Correct C. Speed \(=6.44\ \text{m s}^{-1}\); average power \(=1.68\times10^{2}\ \text{W}\)

D. Speed \(=7.30\ \text{m s}^{-1}\); average power \(=2.05\times10^{2}\ \text{W}\)

Correct Answer: C

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Question 17 View Details

A copper rod (thermal conductivity \(k_{Cu}=400\ \text{W m}^{-1}\text{K}^{-1}\)) of length \(0.50\ \text{m}\) and cross‑sectional area \(1.0\times10^{-4}\ \text{m}^2\) is joined to an aluminium rod (thermal conductivity \(k_{Al}=205\ \text{W m}^{-1}\text{K}^{-1}\)) of length \(0.30\ \text{m}\) and the same cross‑section. The far ends of the copper and aluminium rods are kept at \(100^{\circ}\text{C}\) and \(20^{\circ}\text{C}\) respectively. The junction loses heat to the surroundings at \(25^{\circ}\text{C}\) by convection with heat‑transfer coefficient \(h = 10\ \text{W m}^{-2}\text{K}^{-1}\) over an area of \(0.020\ \text{m}^2\). Assuming steady‑state conditions, (a) calculate the rate of heat transfer through the system, and (b) determine the temperature at the junction.

A. Heat transfer \(=2.80\ \text{W}\); junction temperature \(\approx 65.0^{\circ}\text{C}\)

Correct B. Heat transfer \(=2.49\ \text{W}\); junction temperature \(\approx 68.9^{\circ}\text{C}\)

C. Heat transfer \(=3.10\ \text{W}\); junction temperature \(\approx 72.5^{\circ}\text{C}\)

D. Heat transfer \(=1.85\ \text{W}\); junction temperature \(\approx 60.2^{\circ}\text{C}\)

Correct Answer: B

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Question 18 View Details

Two forces act on a point. Force \(\mathbf{F}_1 = 30\ \text{N}\) acts due east, and force \(\mathbf{F}_2 = 40\ \text{N}\) acts at \(60^{\circ}\) north of east. Find the magnitude of the resultant force and its direction measured north of east.

A. Resultant magnitude \(=62.0 \ \text{N}\); direction \(=30.0^{\circ}\) north of east

B. Resultant magnitude \(=68.4 \ \text{N}\); direction \(=41.3^{\circ}\) north of east

Correct C. Resultant magnitude \(=60.8\ \text{N}\); direction \(=34.7^{\circ}\) north of east

D. Resultant magnitude \(=55.2 \ \text{N}\); direction \(=28.1^{\circ}\) north of east

Correct Answer: C

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Question 19 View Details

A \(10\ \text{kg}\) block rests on a plane inclined at \(25^{\circ}\) to the horizontal. The coefficients of static and kinetic friction are \(\mu_s = 0.40\) and \(\mu_k = 0.30\) respectively. A rope parallel to the incline pulls the block upward. (a) Determine the minimum tension in the rope required to start moving the block up the incline. (b) Once the block moves at constant speed of \(2.0\ \text{m s}^{-1}\), find the power supplied by the rope.

A. Minimum tension \(=68.2 \ \text{N}\); power at 2.0 m s⁻¹ \(=1.10\times10^{2} \ \text{W}\)

Correct B. Minimum tension \(=76.9\ \text{N}\); power at 2.0 m s⁻¹ \(=1.36\times10^{2}\ \text{W}\)

C. Minimum tension \(=73.0 \ \text{N}\); power at 2.0 m s⁻¹ \(=1.25\times10^{2} \ \text{W}\)

D. Minimum tension \(=84.5 \ \text{N}\); power at 2.0 m s⁻¹ \(=1.50\times10^{2} \ \text{W}\)

Correct Answer: B

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Question 20 View Details

A car travels \(60\ \text{km}\) north and then \(80\ \text{km}\) east, taking a total time of \(2.0\ \text{h}\). (a) Find the magnitude of the displacement of the car. (b) Calculate the average speed of the car over the whole journey.

A. Displacement magnitude \(=120\ \text{km}\); average speed \(=70\ \text{km h}^{-1}\)

B. Displacement magnitude \(=140\ \text{km}\); average speed \(=60\ \text{km h}^{-1}\)

Correct C. Displacement magnitude \(=100\ \text{km}\); average speed \(=70\ \text{km h}^{-1}\)

D. Displacement magnitude \(=100\ \text{km}\); average speed \(=80\ \text{km h}^{-1}\)

Correct Answer: C

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Question 21 View Details

A class‑I lever is used to lift a load. The effort of \(120\) N is applied at a distance of \(0.80\) m from the fulcrum, while the load is attached \(0.20\) m on the opposite side. Because of friction at the fulcrum the mechanical efficiency of the lever is \(75\%\). What is the maximum weight of the load (in newtons) that can be lifted?

A. 420 N

B. 300 N

C. 480 N

Correct D. 360 N

Correct Answer: D

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Question 22 View Details

A circular coil of radius \(0.10\ \text{m}\) contains \(200\) turns and is placed in a uniform magnetic field that is initially \(0.5\ \text{T}\) and directed perpendicular to the plane of the coil. Over a period of \(0.04\ \text{s}\) the field strength is increased uniformly to \(0.8\ \text{T}\) while the coil rotates at a constant angular speed of \(30\ \text{rad s}^{-1}\) about an axis through its centre lying in the plane of the coil. Determine the maximum magnitude of the induced emf (in volts) in the coil during this interval.

A. 1.45×10^2 V

Correct B. 1.23×10^2 V

C. 1.05×10^2 V

D. 9.80×10^1 V

Correct Answer: B

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Question 23 View Details

A point charge \(+5.0\ \mu\text{C}\) is placed \(0.12\ \text{m}\) from the centre of an isolated conducting sphere of radius \(0.04\ \text{m}\) that is initially uncharged. (a) Find the magnitude of the total induced charge on the surface of the sphere. (b) Find the magnitude of the electric field just outside the sphere's surface after induction. (c) Find the electrostatic potential of the sphere relative to infinity.

A. a) 1.0 μC; b) 9.4×10^5 N C⁻¹; c) -3.7×10^4 V

B. a) 2.5 μC; b) 8.1×10^6 N C⁻¹; c) -4.2×10^5 V

Correct C. a) 1.7 μC; b) 9.4×10^6 N C⁻¹; c) -3.7×10^5 V

D. a) 0.85 μC; b) 1.2×10^7 N C⁻¹; c) -2.9×10^5 V

Correct Answer: C

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Question 24 View Details

An electron in a hydrogen atom makes a transition from the \(n=5\) level to the \(n=2\) level, emitting a photon. (a) Calculate the wavelength of the photon in vacuum. (b) The photon then passes through a gas that is moving directly away from the source at a speed of \(2.0\times10^{5}\ \text{m s}^{-1}\). Assuming the speed is much less than the speed of light, determine the observed wavelength after the Doppler shift. (c) Determine the energy difference between the two levels in electron‑volts.

A. a) 410 nm; b) 410.5 nm; c) 2.45 eV

B. a) 438 nm; b) 438.5 nm; c) 2.70 eV

C. a) 450 nm; b) 450.2 nm; c) 3.10 eV

Correct D. a) 434 nm; b) 434.3 nm; c) 2.86 eV

Correct Answer: D

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Question 25 View Details

A particle is displaced \(5.0\ \text{m}\) due east and then \(3.0\ \text{m}\) at \(60^{\circ}\) north of east. Find the magnitude of the resultant displacement (in metres) and its direction measured as the angle north of east.

A. 7.0 m, 45° north of east

B. 6.5 m, 15° north of east

Correct C. 7.0 m, 22° north of east

D. 8.1 m, 30° north of east

Correct Answer: C

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