ENGAA 2019

• A.0
• B.$2\sqrt{7}$
• C.$4\sqrt{7}$
• D.$2\sqrt{21}$
• E.10
• F.$4\sqrt{21}$
• G.20

Answer: F

The current-voltage graph for a diode is shown.

The diode is connected in series with a resistor and a 6.0 V battery. The current in the circuit is 8.0 mA.
What is the resistance of the resistor?
(Assume that the battery has negligible resistance.)

• A.$0.15\Omega$
• B.$0.60 \Omega$
• C.$0.75\Omega$
• D.$4.8\Omega$
• E.$150 \Omega$
• F.$600 \Omega$
• G.$750 \Omega$

Answer: F

• A.$x=-2\pm2\sqrt{\frac{3-y}{4}}$
• B.$x=-2\pm2\sqrt{\frac{4-y}{3}}$
• C.$x=1\pm\sqrt{\frac{3-y}{4}}$
• D.$x=1\pm2\sqrt{\frac{3-y}{4}}$
• E.$x=2\pm2\sqrt{\frac{3-y}{4}}$
• F.$x=2\pm2\sqrt{\frac{4-y}{3}}$
• G.$x=2\pm2\sqrt{\frac{3+y}{4}}$

Answer: E

Two electromagnetic waves P and Q travel in a vacuum and the ratio of their wavelengths is:

$$\frac{\text{wavelength of P}}{\text{wavelength of Q}} = 1.0 \times 10^8$$

Which row in the table shows the ratio of their speeds, the ratio of their frequencies, and identifies the possible natures of P and Q?

• A.speed of P speed of Q: 1.0, frequency of P frequency of Q: $1.0 \times 10^{-8}$, nature of P: microwave, nature of Q: X-ray
• B.speed of P speed of Q: 1.0, frequency of P frequency of Q: $1.0 \times 10^{-8}$, nature of P: microwave, nature of Q: radio wave
• C.speed of P speed of Q: 1.0, frequency of P frequency of Q: $1.0 \times 10^8$, nature of P: infrared, nature of Q: ultraviolet
• D.speed of P speed of Q: 1.0, frequency of P frequency of Q: $1.0 \times 10^8$, nature of P: visible light, nature of Q: infrared
• E.speed of P speed of Q: $1.0 \times 10^8$, frequency of P frequency of Q: 1.0, nature of P: gamma, nature of Q: X-ray
• F.speed of P speed of Q: $1.0 \times 10^8$, frequency of P frequency of Q: 1.0, nature of P: gamma, nature of Q: infrared
• G.speed of P speed of Q: $1.0 \times 10^8$, frequency of P frequency of Q: $1.0 \times 10^{16}$, nature of P: infrared, nature of Q: radio wave
• H.speed of P speed of Q: $1.0 \times 10^8$, frequency of P frequency of Q: $1.0 \times 10^{16}$, nature of P: visible light, nature of Q: ultraviolet

Answer: A

• A.20%
• B.24%
• C.44%
• D.120%
• E.224%
• F.240%
• G.400%

Answer: C

• A.40 m
• B.50 m
• C.60 m
• D.400 m
• E.500 m
• F.600 m

Answer: A

• A.1
• B.2
• C.5
• D.6
• E.9
• F.16

Answer: E

• A.60 W
• B.300 W
• C.6000 W
• D.24000 W
• E.120000 W
• F.9600000 W

Answer: A

• A.$\frac{12x^3-8x^2-7x-1}{x(3x-1)(x-1)}$
• B.$\frac{4x^2+4x-1}{x(x+1)}$
• C.$\frac{4x^2+4x+1}{x(x+1)}$
• D.$\frac{4x^2-4x-1}{x(x-1)}$
• E.$\frac{4x^2-4x+1}{x(x-1)}$
• F.$\frac{12x^3-8x^2-x+1}{x(3x-1)(x-1)}$

Answer: D

Two tanks of water are connected by a solid cylindrical copper bar of length $l$ and diameter $d$.
The bar is insulated.
One tank contains water at $90 \text{°C}$ and the other tank contains water at temperature $\theta$.

For which of the following conditions is thermal energy conducted along the bar at the lowest rate?

• A.$l/m$: 0.40, $d/cm$: 4.0, $\theta/\text{°C}$: 20
• B.$l/m$: 0.40, $d/cm$: 4.0, $\theta/\text{°C}$: 40
• C.$l/m$: 0.40, $d/cm$: 8.0, $\theta/\text{°C}$: 20
• D.$l/m$: 0.40, $d/cm$: 8.0, $\theta/\text{°C}$: 40
• E.$l/m$: 0.80, $d/cm$: 4.0, $\theta/\text{°C}$: 20
• F.$l/m$: 0.80, $d/cm$: 4.0, $\theta/\text{°C}$: 40
• G.$l/m$: 0.80, $d/cm$: 8.0, $\theta/\text{°C}$: 20
• H.$l/m$: 0.80, $d/cm$: 8.0, $\theta/\text{°C}$: 40

Answer: F

• A.48
• B.81
• C.96
• D.108
• E.144

Answer: B

The radioactive isotope X becomes the stable isotope Y after a succession of decays involving only the emission of alpha and beta ($\beta^-$) particles.
During the decay of one nucleus from X to Y, a total of seven particles are emitted. It is known that more of these particles are alpha particles than beta particles.
The atomic number of X is Z and the mass number of X is A.
Which row in the table could give the atomic number and the mass number of Y?

• A.atomic number of Y: Z-2, mass number of Y: A-12
• B.atomic number of Y: Z-5, mass number of Y: A-8
• C.atomic number of Y: Z-8, mass number of Y: A-20
• D.atomic number of Y: Z-10, mass number of Y: A-24
• E.atomic number of Y: Z-11, mass number of Y: A-16

Answer: C

The diagram shows a right-angled triangle, with sides of length $x + 4$, $2x + 2$ and $3x$, all in cm.

[diagram not to scale]
What is the area, in $\text{cm}^2$, of the triangle?

• A.10
• B.12
• C.28
• D.36
• E.40
• F.54
• G.70

Answer: F

• A.2.0 N
• B.4.0 N
• C.8.0 N
• D.24 N
• E.28 N
• F.56 N

Answer: C

• A.$2\frac{2}{3}$
• B.$4\frac{1}{2}$
• C.$5\frac{1}{3}$
• D.8
• E.14

Answer: D

In the following circuit, all five resistors have the same resistance.

The reading on the voltmeter is 1.0V.
What is the voltage across the battery?

• A.4.0 V
• B.5.0 V
• C.6.0 V
• D.7.0 V
• E.8.0 V
• F.9.0 V
• G.10 V

Answer: E

The diagram shows two congruent right-angled triangles PQR and TSR with right angles at Q and S, respectively.

[diagram not to scale]
PQ = TS = 3 cm
QR = SR = 4 cm
PRT is a straight line.
What is the length, in cm, of QS?

• A.4
• B.$3\sqrt{2}$
• C.5.2
• D.$4\sqrt{2}$
• E.6.4
• F.8.2
• G.10

Answer: E

A block is designed with a cylindrical channel to accommodate a hot-water pipe. The block is 100 cm long and it has a square cross-section of side 22.0 cm with a cylindrical hole in the middle, as shown in the diagram:

[diagram not to scale]
The diameter of the cylindrical hole is 14.0 cm and the density of the material from which the block is made is $0.100 \text{g cm}^{-3}$.
What is the mass of the block?
(take $\pi$ to be $\frac{22}{7}$)

• A.1.32 kg
• B.3.30 kg
• C.13.2 kg
• D.33.0 kg
• E.132 kg
• F.330 kg
• G.1320 kg
• H.3300 kg

Answer: B

A solid pyramid has a square base of side length 12cm and a vertical height of h cm.

[diagram not to scale]
The volume of the pyramid, in $\text{cm}^3$, is equal to the total surface area of the pyramid, in $\text{cm}^2$.
What is the value of h?
(volume of pyramid = $\frac{1}{3} \times \text{area of base} \times \text{vertical height})$

• A.$\frac{72}{35}$
• B.$2\sqrt{3}$
• C.6
• D.$\frac{144}{23}$
• E.8
• F.$2\sqrt{21}$

Answer: E

• A.The sample contains only isotope Y.
• B.1:7
• C.1:4
• D.1:3
• E.7:4

Answer: B

• A.4
• B.12
• C.21
• D.25
• E.27
• F.30

Answer: C

• A.$6.48 \times 10^4 \text{m}^3$
• B.$7.20 \times 10^4 \text{m}^3$
• C.$8.00 \times 10^4 \text{m}^3$
• D.$6.48 \times 10^7 \text{m}^3$
• E.$7.20 \times 10^7 \text{m}^3$
• F.$8.00 \times 10^7 \text{m}^3$

Answer: C

• A.-9
• B.-3
• C.-1
• D.1
• E.3
• F.9

Answer: B

A car P of mass 1000 kg is travelling north at $30\text{m s}^{-1}$ along a straight, horizontal road when it hits another car Q which is directly ahead of P and travelling in the same direction. Car Q has a mass of 500 kg and is travelling at $20 \text{m s}^{-1}$.
The collision lasts for 0.20 s and immediately after the collision car Q is moving north at $30 \text{m s}^{-1}$.
What is the speed of P immediately after the collision and what is the size of the average resultant force that acts on Q during the collision?
(Assume that no external forces act on the cars during the collision.)

• A.speed of P / $\text{m s}^{-1}$: 20, average force on Q / N: 25000
• B.speed of P / $\text{m s}^{-1}$: 20, average force on Q / N: 50000
• C.speed of P / $\text{m s}^{-1}$: 20, average force on Q / N: 100 000
• D.speed of P / $\text{m s}^{-1}$: 20, average force on Q / N: 125000
• E.speed of P / $\text{m s}^{-1}$: 25, average force on Q / N: 25000
• F.speed of P / $\text{m s}^{-1}$: 25, average force on Q / N: 50000
• G.speed of P / $\text{m s}^{-1}$: 25, average force on Q / N: 100 000
• H.speed of P / $\text{m s}^{-1}$: 25, average force on Q / N: 125000

Answer: E

• A.-7
• B.-5
• C.-1
• D.1
• E.5
• F.7

Answer: B

• A.0.05 V
• B.0.20 V
• C.0.80 V
• D.3.2 V
• E.5.0 V
• F.20 V

Answer: C

• A.$\frac{1}{2}$ or $\frac{1}{3}$
• B.$\frac{1}{\sqrt{3}}$ or $\frac{1}{2\sqrt{2}}$
• C.$\frac{\sqrt{3}}{2}$ or $\frac{2\sqrt{2}}{3}$
• D.$\sqrt{3}$ or $2\sqrt{2}$
• E.3 or 2

Answer: D

A uniform square trap door of side 0.80 m and mass 14kg has a smooth hinge at one edge and is held open at an angle of 30° to the horizontal. It is supported by a single rigid rod placed so that it meets the surface of the trap door at 90° at a distance 0.10m from the top edge of the trap door, as shown.

What is the normal contact force exerted on the trap door by the rod?
(gravitational field strength = $10\text{N kg}^{-1}$)

• A.40 N
• B.$35\sqrt{3}$ N
• C.$40\sqrt{3}$ N
• D.80 N
• E.$80\sqrt{3}$ N
• F.$280\frac{\sqrt{3}}{3}$ N

Answer: C

An equilateral triangle of side 8 cm is drawn so that its vertices lie on the circumference of a circle, as shown in the diagram.

What is the total of the three areas shaded in the diagram, in $\text{cm}^2$?

• A.$8(2\pi-3)$
• B.$24 (\pi-\sqrt{3})$
• C.$48(4\pi-\sqrt{3})$
• D.$\frac{16}{3}(4\pi-6-3\sqrt{3})$
• E.$\frac{16}{3}(4\pi-3\sqrt{3})$

Answer: E

Two small loudspeakers are placed side by side 30 cm apart.
They are connected to the same signal generator so that they emit sound of frequency 400 Hz in phase with one another.
The sounds both reach a microphone placed 40 cm directly in front of one of the two loudspeakers as shown.

What is the phase difference between waves from the loudspeakers as they arrive at the microphone?
(speed of sound = $320\text{m s}^{-1}$)

• A.30°
• B.36°
• C.45°
• D.60°
• E.72°
• F.90°
• G.120°

Answer: C

• A.$x=\log_5 \left(\frac{1}{3}\right)$
• B.$x = \log_5 \left(\frac{2}{5}\right)$
• C.$x = \log_5 \left(\frac{3}{5}\right)$
• D.$x=\log_5 \left(\frac{2}{3}\right)$
• E.$x=\log_5 \left(\frac{5}{3}\right)$
• F.$x = \log_5 \left(\frac{5}{2}\right)$

Answer: B

• A.25 m
• B.50 m
• C.320 m
• D.2000 m
• E.3200 m
• F.4000 m

Answer: D

• A.$\frac{1}{3}$
• B.$\frac{11}{7}$
• C.$\frac{11}{6}$
• D.$\frac{13}{6}$
• E.$\frac{13}{3}$

Answer: A

A student has one $300 \Omega$ resistor and another resistor of resistance R.
The student plots a graph of current I against potential difference V for the $300 \Omega$ resistor and then for both resistors connected in parallel.

What is the resistance R?

• A.$3.3\Omega$
• B.$5.0\Omega$
• C.$10\Omega$
• D.$100 \Omega$
• E.$200 \Omega$
• F.$600 \Omega$
• G.$1000 \Omega$

Answer: F

• A.70
• B.162
• C.$\frac{2835}{4}$
• D.3024
• E.5670
• F.15120
• G.22680

Answer: E

• A.$8.0 \times 10^{-5}$ J
• B.$1.7 \times 10^{-4}$ J
• C.$4.0 \times 10^{-4}$ J
• D.$8.0 \times 10^{-3}$ J
• E.$4.0 \times 10^{-2}$ J
• F.$1.6 \times 10^{-2}$ J

Answer: D

• A.15
• B.45
• C.75
• D.105
• E.135

Answer: D

Light travelling in a transparent liquid strikes the surface from below. The angle between the surface of the liquid and the direction of travel of the light is $\alpha$.
The light then travels along the surface between the liquid and the air as shown in the diagram.

Now, light travelling in air strikes the surface from above so that the angle between the surface and the direction of travel of this light is also $\alpha$.
After the light strikes the surface from above, the angle between the surface and the direction of travel of the refracted light is $\beta$.
Which expression gives $\beta$?
(all angles are in degrees)

• A.$\cos\beta = \cos^2\alpha$
• B.$\cos\beta = \cos\alpha \sin^{-1}\left(\frac{1}{\alpha}\right)$
• C.$\sin\beta = \sin^2\alpha$
• D.$\beta = 90 – (90 – \alpha)^2$
• E.$\beta= 0$
• F.$\beta= \alpha$

Answer: A

• A.$x<-1$
• B.$x>-1$
• C.$-1<x< 4$
• D.$x<-1$ or $x > 4$
• E.$x <4$
• F.$x > 4$

Answer: F

The velocity-time graph is for an 80kg person in a lift that is moving vertically upwards.

What is the magnitude of the contact force between the person and the lift floor at the time corresponding to X?
(gravitational field strength = $10\text{Nkg}^{-1}$)

• A.640 N
• B.768 N
• C.800 N
• D.832 N
• E.960 N

Answer: B