ENGAA 2016 D564/11

• A.$x < 4$
• B.$x > 4$
• C.$x < 20$
• D.$x > 20$
• E.$x < 22$
• F.$x > 22$
• G.$x < 28$
• H.$x > 28$

Answer: G

• A.3 alpha
• B.2 alpha and 1 beta
• C.2 alpha and 2 beta
• D.1 alpha and 2 beta
• E.3 beta

Answer: D

• A.$1-2\sqrt{3}\sqrt{2}$
• B.$5-2\sqrt{2}\sqrt{3}$
• C.$2\sqrt{3}-2\sqrt{2}$
• D.1
• E.$5-\sqrt{2}\sqrt{3}$
• F.$13-2\sqrt{2}\sqrt{3}$
• G.$5+2\sqrt{2}\sqrt{3}$
• H.5

Answer: B

The graph shown of quantity $y$ against quantity $x$ represents the motion of a body.
(A diagram shows a straight line graph passing through the origin (0,0) and the point (2.0, 10)).
(The scales on both axes are in the appropriate S.I. units, and the gravitational field strength $g$ is $10 N kg^{-1}$.)
Which two of the following could the graph represent?
1 kinetic energy against velocity for an object of mass 10 kg undergoing free-fall
2 potential energy against height for an object of mass 20 kg being lifted by a constant external force
3 velocity against time for an object of mass 20 kg being accelerated by a resultant force of 100 N
4 work done by an external force of 5N against distance moved for an object of mass 12 kg being moved at constant speed by (and in the direction of) the external force

• A.1 and 2
• B.1 and 3
• C.1 and 4
• D.2 and 3
• E.2 and 4
• F.3 and 4

Answer: F

• A.1:2
• B.2:1
• C.3:4
• D.3:25
• E.4:3
• F.25:3

Answer: C

A uranium-235 nucleus can undergo fission to produce two smaller nuclei.
Which of the diagrams, if any, could represent this process?

• A.none of them
• B.1 only
• C.2 only
• D.3 only
• E.1 and 2 only
• F.1 and 3 only
• G.2 and 3 only
• H.1, 2 and 3

Answer: C

• A.20 years
• B.22 years
• C.30 years
• D.40 years
• E.50 years
• F.52 years

Answer: E

• A.7.2 W
• B.18 W
• C.27 W
• D.45 W
• E.72 W
• F.75 W

Answer: D

• A.£600
• B.£3000
• C.£5400
• D.£6000
• E.£9000
• F.£9600
• G.£12000

Answer: C

• A.$2.5 \times 10^{27}$ W
• B.$1.0 \times 10^{28}$ W
• C.$2.0 \times 10^{28}$ W
• D.$2.5 \times 10^{29}$ W
• E.$1.0 \times 10^{30}$ W
• F.$2.0 \times 10^{30}$ W
• G.$2.5 \times 10^{33}$ W
• H.$1.0 \times 10^{34}$ W

Answer: D

• A.2 km
• B.$2\sqrt{3}$ km
• C.4 km
• D.$2\sqrt{5}$ km
• E.$4\sqrt{2}$ km

Answer: B

• A.900 cm
• B.1200 cm
• C.1800 cm
• D.2400 cm
• E.3600 cm
• F.4800 cm

Answer: E

• A.$\frac{3}{2}$
• B.2
• C.$\frac{81}{16}$
• D.$\frac{27}{14}$
• E.12
• F.16

Answer: F

A motor is used to lift a mass of $5.0 \text{kg}$ using a pulley system as shown in the diagram. The pulley is secured to the roof using a coupling.
The motor needs to cause the mass to accelerate upwards at $0.80 ms^{-2}$.
What is the minimum tension force that the coupling must be able to withstand without breaking?
(The gravitational field strength $g$ is $10 Nkg^{-1}$. The pulley system is frictionless and has negligible mass. The rope has negligible mass and is inextensible.)

• A.4.0 N
• B.8.0 N
• C.46 N
• D.50 N
• E.54 N
• F.92 N
• G.104 N
• H.108 N

Answer: H

In a trapezium PQRS, the parallel sides are PQ and RS.
$PQ = (x-1) cm$, $RS = (x+5) cm$ and the vertical height $QR = x cm$.
The area of the trapezium is $120 cm^2$.
What is the length of RS?

• A.9 cm
• B.10 cm
• C.11 cm
• D.12 cm
• E.15 cm
• F.17 cm

Answer: E

A heater is connected in series with a resistor and a 6.0 V battery in the circuit shown.
The total resistance of the circuit is 15 $\Omega$. In 3.0 minutes, 180 J of electrical energy is transferred into other forms in the heater.
How much charge flows through the heater in the 3.0 minutes and what is the voltage across the heater?

• A.charge / C: 1.2, voltage / V: 150
• B.charge / C: 1.2, voltage / V: 216
• C.charge / C: 7.5, voltage / V: 0.041
• D.charge / C: 7.5, voltage / V: 24
• E.charge / C: 72, voltage / V: 0.40
• F.charge / C: 72, voltage / V: 2.5
• G.charge / C: 450, voltage / V: 0.40
• H.charge / C: 450, voltage / V: 2.5

Answer: F

• A.$b = \pm \sqrt{\frac{a+2}{3a+1}}$
• B.$b = \pm \sqrt{\frac{a+2}{3a-1}}$
• C.$b = \pm \sqrt{\frac{2-a}{3a+1}}$
• D.$b = \pm \sqrt{\frac{2-a}{3a-1}}$
• E.$b = \pm \sqrt{\frac{3}{3a+1}}$
• F.$b = \pm \sqrt{\frac{3}{3a-1}}$

Answer: B

A cubic block has a hole through it with a square cross-section. The dimensions are shown on the diagram. The weight of the block is 30 N. The outer cube has a side length of 10 cm, and the inner square hole has a side length of 5.0 cm.
What is the density of the material from which the block is made?
(The gravitational field strength $g$ is $10 N kg^{-1}$.)

• A.$0.30 g cm^{-3}$
• B.$0.40 g cm^{-3}$
• C.$0.60 g cm^{-3}$
• D.$1.2 g cm^{-3}$
• E.$3.0 g cm^{-3}$
• F.$4.0 g cm^{-3}$
• G.$6.0 g cm^{-3}$
• H.$12 g cm^{-3}$

Answer: F

A thin rectangular sheet of metal 10 m by 5 m is made into an open ended cylinder by joining the edges PS and QR.
The height of the cylinder is 10 m.
What is the volume, in cubic metres, enclosed by this cylinder?

• A.$\frac{5}{2\pi}$
• B.$\frac{25}{4\pi}$
• C.$\frac{125}{2\pi}$
• D.$62.5\pi$
• E.$\frac{125}{\pi}$
• F.$250\pi$

Answer: C

The diagram shows four solid steel balls P, Q, R and S which are of identical size.
Balls P and R have shiny surfaces. Balls Q and S have dull surfaces.
Balls P and Q are in a room at 20 °C. Balls R and S are in a room at 40 °C.
The temperature of each ball at a given moment in time is shown on the diagram.
(Diagram shows: Ball P, shiny, 30°C in a 20°C room. Ball Q, dull, 30°C in a 20°C room. Ball R, shiny, 40°C in a 40°C room. Ball S, dull, 40°C in a 40°C room.)
Which two balls lose thermal energy by convection, and which ball emits thermal radiation at the greatest rate?

• A.lose thermal energy by convection: P and Q, greatest rate of emission of thermal radiation: P
• B.lose thermal energy by convection: P and Q, greatest rate of emission of thermal radiation: Q
• C.lose thermal energy by convection: P and Q, greatest rate of emission of thermal radiation: R
• D.lose thermal energy by convection: P and Q, greatest rate of emission of thermal radiation: S
• E.lose thermal energy by convection: R and S, greatest rate of emission of thermal radiation: P
• F.lose thermal energy by convection: R and S, greatest rate of emission of thermal radiation: Q
• G.lose thermal energy by convection: R and S, greatest rate of emission of thermal radiation: R
• H.lose thermal energy by convection: R and S, greatest rate of emission of thermal radiation: S

Answer: D

• A.$3 - \frac{2}{x}$
• B.$3 + \frac{2}{x}$
• C.$4 - \frac{2}{x}$
• D.$4 + \frac{2}{x}$
• E.$5 - \frac{2}{x}$
• F.$5 + \frac{2}{x}$

Answer: A

The diagram shows the velocity-time graph for an object travelling in a straight line over a period of 30 s.
(The graph shows velocity starting at 8.0 m/s at t=0, decreasing linearly to 0 m/s at t=20 s, and further decreasing linearly to -2.0 m/s at t=30 s.)
What total distance did the object travel in the 30s, how far from its starting position was it at the end of the 30s, and what was its average speed over the 30s?

• A.total distance travelled / m: 90, distance from starting position / m: 70, average speed / ms⁻¹: 3.0
• B.total distance travelled / m: 90, distance from starting position / m: 70, average speed / ms⁻¹: 5.0
• C.total distance travelled / m: 90, distance from starting position / m: 90, average speed / ms⁻¹: 3.0
• D.total distance travelled / m: 90, distance from starting position / m: 90, average speed / ms⁻¹: 5.0
• E.total distance travelled / m: 180, distance from starting position / m: 140, average speed / ms⁻¹: 5.0
• F.total distance travelled / m: 180, distance from starting position / m: 140, average speed / ms⁻¹: 6.0
• G.total distance travelled / m: 180, distance from starting position / m: 180, average speed / ms⁻¹: 5.0
• H.total distance travelled / m: 180, distance from starting position / m: 180, average speed / ms⁻¹: 6.0

Answer: A

• A.$\frac{3}{20}$
• B.$\frac{9}{37}$
• C.$\frac{4}{15}$
• D.$\frac{16}{37}$
• E.$\frac{32}{57}$

Answer: D

• A.$\frac{X}{9X-Y} \times 100$
• B.$\frac{X}{9Y-X} \times 100$
• C.$\frac{Y}{9X-Y} \times 100$
• D.$\frac{Y}{9Y-X} \times 100$
• E.$\frac{X}{9X+Y} \times 100$
• F.$\frac{X}{9Y+X} \times 100$
• G.$\frac{Y}{9X+Y} \times 100$
• H.$\frac{Y}{9Y+X} \times 100$

Answer: G

• A.$3^9$
• B.$3^{-2n}$
• C.$3^{2-2n}$
• D.$3^{4n}$
• E.$3^{6n-2}$
• F.$3^6$

Answer: D

When a stationary uranium-238 nucleus decays by alpha emission it forms a nucleus of thorium-234. The total kinetic energy produced by the decay is $E$.
What is the kinetic energy of the alpha particle?

• A.$\frac{4E}{238}$
• B.$\frac{4E}{234}$
• C.$\frac{E}{2}$
• D.$\frac{234E}{238}$
• E.$E$

Answer: D

In the diagram below, PQRS is part of a regular polygon.
The polygon has $n$ sides.
The side PQ is extended to T such that PQT is a straight line.
The length of RQ is the same as the length of RT.
Find an equation for $n$ in terms of $x$, where $x$ is the size of angle $\angle QRT$ in degrees.

• A.$n = \frac{180}{x-90}$
• B.$n = \frac{180-x}{720}$
• C.$n = \frac{360-x}{90}$
• D.$n = \frac{360}{180-x}$
• E.$n = \frac{720}{180-x}$
• F.$n = \frac{720}{360-x}$
• G.$n = \frac{360}{360-x}$

Answer: E

A student carries out an experiment to measure the speed of sound. A loudspeaker that emits sound in all directions is placed between two buildings that are 128 m apart as shown. The student and loudspeaker are 48 m from one of the buildings.
The loudspeaker is connected to a signal generator that causes it to emit regular clicks. The student notices that each click results in two echoes, one from each building. The rate at which the clicks are produced is gradually increased from zero until each echo coincides with a new click being emitted by the loudspeaker.
What is the frequency of emission of clicks when this happens?
(The speed of sound in air = $320 ms^{-1}$.)

• A.2.0 Hz
• B.2.5 Hz
• C.3.3 Hz
• D.4.0 Hz
• E.5.3 Hz
• F.6.7 Hz
• G.10 Hz

Answer: G

• A.$p = -1 \pm \frac{\sqrt{6}}{3}$
• B.$p = 1$ or $p = -3$
• C.$p = 1$
• D.$p = 1 \pm \sqrt{7}$
• E.there are no values for $p$

Answer: C

A parachutist is falling at terminal speed with his parachute open. The diagrams show, separately, the vertical forces acting on the parachute and the vertical forces acting on the parachutist.
The letters L, M, N, P, Q and R represent the magnitude of each force as indicated.

Consider the following equations:
Equation 1: $L = M+N$
Equation 2: $R = P+Q$
Equation 3: $L = Q$
Equation 4: $N = P$
Equation 5: $M+R = L+Q$
Which of these equations, if any, is/are the direct result of the application of Newton's Third Law to this situation?

• A.none of them
• B.3 only
• C.4 only
• D.5 only
• E.1 and 2 only
• F.3 and 4 only
• G.1, 2 and 5 only
• H.1, 2, 3, 4 and 5

Answer: C

• A.$x^2 + y^2 - 4x + 6y + 4 = 0$
• B.$x^2 + y^2 - 4x + 6y + 9 = 0$
• C.$x^2 + y^2 + 4x - 6y + 4 = 0$
• D.$x^2 + y^2 + 4x - 6y + 9 = 0$
• E.$x^2 + y^2 - 6x - 4y + 9 = 0$
• F.$x^2 + y^2 - 6x + 4y + 4 = 0$
• G.$x^2 + y^2 + 6x - 4y + 4 = 0$
• H.$x^2 + y^2 + 6x + 4y + 9 = 0$

Answer: C

A crate has a total mass of 800 kg, including its contents. A helicopter of mass 4200 kg is carrying the crate using a light inextensible rope as shown.
The helicopter and crate are accelerating upwards at $2.0 ms^{-2}$.
What is the tension in the rope?
(The gravitational field strength $g$ is $10 Nkg^{-1}$; air resistance can be ignored.)

• A.6400 N
• B.8000 N
• C.9600 N
• D.18000 N
• E.40000 N
• F.42000 N
• G.50000 N
• H.60000 N

Answer: C

• A.$8(1+\sqrt{2})$
• B.$8(1-\sqrt{2})$
• C.$8(2+\sqrt{2})$
• D.$8(2-\sqrt{2})$
• E.16
• F.$\frac{8\sqrt[5]{4}}{\sqrt[5]{4}-1}$
• G.$\frac{8\sqrt[5]{4}}{\sqrt[5]{4}+1}$

Answer: C

A shopper pushes a supermarket trolley a distance of 15 m in a straight line across a level, horizontal surface. The shopper applies a constant force of 50 N at an angle of 37° below the horizontal. The total weight of the trolley and its contents is 350 N.
What is the magnitude of the total vertical force that the surface exerts on the trolley and how much work is done by the pushing force?
(You may use the approximations $\sin 37° = 0.60$; $\cos 37° = 0.80$.)

• A.vertical force / N: 380, work done / J: 600
• B.vertical force / N: 380, work done / J: 750
• C.vertical force / N: 390, work done / J: 450
• D.vertical force / N: 390, work done / J: 750
• E.vertical force / N: 400, work done / J: 450
• F.vertical force / N: 400, work done / J: 600

Answer: A

Tangents are drawn from a point P to a circle of radius 10 cm.
The centre of the circle is C and the distance PC is 20 cm.
Which one of the following is an expression for the shaded area in square centimetres?

• A.$\frac{100}{3}(3\sqrt{3}-\pi)$
• B.$\frac{100}{3}(3\sqrt{5}-\pi)$
• C.$\frac{50}{3}(6\sqrt{3}-\pi)$
• D.$\frac{50}{3}(6\sqrt{5}-\pi)$
• E.$\frac{50}{3}(\sqrt{3}-2\pi)$
• F.$\frac{50}{3}(2\pi-\sqrt{3})$

Answer: A

A plank of non-uniform density which has a mass of 15 kg is used to make a see-saw. A pivot is placed under the centre of the plank as shown on the diagram.
A boy of mass 35 kg sits at one end of the plank with his centre of gravity 1.20 m from the pivot. The see-saw balances when a woman of mass 60 kg sits on the plank on the other side of the pivot. Her centre of gravity is 0.80 m from the pivot.
Where is the centre of gravity of the plank and what is the magnitude of the force between the pivot and the plank?
(The gravitational field strength $g$ is $10 N kg^{-1}$.)

• A.distance from pivot: 0.40 m on left of pivot, force / N: 100
• B.distance from pivot: 0.40 m on left of pivot, force / N: 1100
• C.distance from pivot: at the pivot, force / N: 100
• D.distance from pivot: at the pivot, force / N: 1100
• E.distance from pivot: 0.20 m on right of pivot, force / N: 100
• F.distance from pivot: 0.20 m on right of pivot, force / N: 1100
• G.distance from pivot: 0.40 m on right of pivot, force / N: 100
• H.distance from pivot: 0.40 m on right of pivot, force / N: 1100

Answer: H

• A.$\cos \theta = -\frac{3}{5}$ or $\frac{1}{2}$
• B.$\cos \theta = -\frac{3}{5}$ or $\frac{1}{2}$
• C.$\cos \theta = \frac{3}{5}$ or $\frac{1}{2}$
• D.$\cos \theta = \frac{3}{5}$ or $-\frac{1}{2}$

Answer: D

A car of mass 200 kg on a fairground ride travels at a speed of $5.0 m s^{-1}$ at point X. The car is allowed to move down a sloping section of track without any energy input. The heights above the ground of points X and Y are shown. When the car reaches point Y its speed is $9.0 m s^{-1}$.
(Diagram shows point X at height 8.0 m and point Y at height 2.0 m.)
How much energy is transferred in overcoming resistive forces as the car travels from X to Y?

• A.3900 J
• B.6400 J
• C.7900 J
• D.10400 J
• E.11200 J

Answer: B

• A.no values of $a$
• B.$-4\sqrt{2} < a < 4\sqrt{2}$
• C.$a < -4\sqrt{2}, a > 4\sqrt{2}$
• D.$-4 < a < 8$
• E.$a < -4, a > 8$
• F.$-8 < a < 4$
• G.$a < -8, a > 4$
• H.all values of $a$

Answer: G

The diagram shows a uniform, solid, heavy cube with side $d$. The cube rests with one of its edges in contact with a table that is perfectly level. A horizontal force $P$ acts on another edge of the cube, and the cube is stationary. The cube is tilted at an angle of 30° to the horizontal.
Below are four statements about the forces on the cube.
1 It is possible that there is no frictional force between the cube and the table.
2 There must be a frictional force acting to the left between the cube and the table.
3 There must be a frictional force acting to the right between the cube and the table.
4 Force $P$ has a clockwise moment about the edge in contact with the table equal to $P \times d$.
Which of the statements is/are correct?

• A.1 only
• B.2 only
• C.3 only
• D.1 and 4 only
• E.2 and 4 only
• F.3 and 4 only

Answer: B

The straight line with equation $y = mx + 3$, where $m > 0, m ≠ 1$, is perpendicular to the line with equation $y = px + 2$.
The lines cut the x-axis at the points L and M respectively. The length of LM is 5 units.
What is the value of $m+p$ given that $m > 1$?

• A.$-\frac{8}{3}$
• B.$-\frac{13}{6}$
• C.$-\frac{5}{6}$
• D.$\frac{5}{6}$
• E.$\frac{13}{6}$
• F.$\frac{8}{3}$

Answer: D

The diagram shows two identical blocks, each of mass $m$, in two different arrangements.
(Arrangement 1 shows two blocks stacked vertically. The bottom block has height b. The top block has height a.)
(Arrangement 2 shows the two blocks side by side on the ground.)
Which expression gives:
$\left[ \text{gravitational potential energy of arrangement 2} \right] - \left[ \text{gravitational potential energy of arrangement 1} \right]$ ?
(g is the gravitational field strength.)

• A.$2mg(a-b)$
• B.$2mg(b-a)$
• C.$-mg(b+a)$
• D.$mg(a+b)$
• E.$\frac{3}{2}mg(a-b)$
• F.$\frac{1}{2}mg(a-b)$

Answer: A

• A.$x \le -a, x \ge a$
• B.$-a \le x \le a$
• C.$x \le -a, 0 \le x \le a$
• D.$-a \le x \le 0, x \ge a$
• E.$x \le -\frac{a}{3}, x \ge \frac{a}{3}$
• F.$-\frac{a}{3} \le x \le \frac{a}{3}$
• G.$x \le -\frac{a}{\sqrt{3}}, x \ge \frac{a}{\sqrt{3}}$
• H.$-\frac{a}{\sqrt{3}} \le x \le \frac{a}{\sqrt{3}}$

Answer: G

An object is fired vertically upwards from the ground at time $t = 0 s$ in still air at a speed of $8.0 ms^{-1}$.
On the way up, what is the height of the object above the ground when it has a speed of $2.0 ms^{-1}$, and at what time does it reach this height on the way down?
(The gravitational field strength $g$ is $10 Nkg^{-1}$. Air resistance can be ignored.)

• A.height / m: 2.4, time / s: 0.60
• B.height / m: 2.4, time / s: 0.64
• C.height / m: 2.4, time / s: 1.0
• D.height / m: 2.4, time / s: 2.0
• E.height / m: 3.0, time / s: 0.60
• F.height / m: 3.0, time / s: 0.64
• G.height / m: 3.0, time / s: 1.0
• H.height / m: 3.0, time / s: 2.0

Answer: G

• A.$y = -3-(x-4)^2$
• B.$y = -3+(x+4)^2$
• C.$y = 3-(x+4)^2$
• D.$y = 3+(x-4)^2$
• E.$y = -5-(x-4)^2$
• F.$y = -5+(x+4)^2$
• G.$y = 5-(x+4)^2$
• H.$y = 5+(x-4)^2$

Answer: E

The diagram shows a ball P, of mass 4.0 kg, moving to the right at $10 ms^{-1}$ directly towards a stationary ball Q, of mass 2.0 kg.
The balls collide but do not join together. Immediately after the collision ball Q moves at $10 ms^{-1}$ to the right.
What is the velocity of ball P immediately after the collision, and how much kinetic energy in total is lost during the collision?

• A.velocity of ball P after collision: 0, kinetic energy lost during collision / J: 50
• B.velocity of ball P after collision: 0, kinetic energy lost during collision / J: 150
• C.velocity of ball P after collision: $10 ms^{-1}$ to the left, kinetic energy lost during collision / J: 50
• D.velocity of ball P after collision: $10 ms^{-1}$ to the left, kinetic energy lost during collision / J: 150
• E.velocity of ball P after collision: $5.0 ms^{-1}$ to the right, kinetic energy lost during collision / J: 50
• F.velocity of ball P after collision: $5.0 ms^{-1}$ to the right, kinetic energy lost during collision / J: 150

Answer: E

• A.$x < \frac{1}{2}, x > 4$
• B.$\frac{1}{2} < x < 4$
• C.$x < -2, -\frac{1}{\sqrt{2}} < x < \frac{1}{\sqrt{2}}, x > 2$
• D.$-2 < x < -\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} < x < 2$
• E.$-2 < x < 2$

Answer: C

• A.$5.0 ms^{-2}$
• B.$7.25 ms^{-2}$
• C.$7.5 ms^{-2}$
• D.$8.0 ms^{-2}$
• E.$10 ms^{-2}$
• F.$10.5 ms^{-2}$

Answer: A

• A.0
• B.5
• C.25
• D.69
• E.133

Answer: B

An object of mass 20 kg is pulled up a rough plane inclined at 30° to the horizontal by a light, inextensible cable attached via a frictionless pulley to a freely-falling 30 kg mass. The acceleration of the object along the plane is $2.5 ms^{-2}$.
$\cos 30° = \sin 60° = \frac{\sqrt{3}}{2}$
$\sin 30° = \cos 60° = \frac{1}{2}$
What is the frictional force between the object and the plane?
(Air resistance and the mass of the pulley can be ignored. The gravitational field strength $g$ is $10 N kg^{-1}$.)

• A.25 N
• B.50 N
• C.75 N
• D.100 N
• E.150 N
• F.175 N
• G.250 N

Answer: C

• A.4
• B.8
• C.10
• D.11
• E.14
• F.20

Answer: A

• A.22 kg
• B.34 kg
• C.40 kg
• D.50 kg
• E.200 kg
• F.210 kg

Answer: E

• A.no values of $k$
• B.$-12 < k < 15$
• C.$15 < k < 20$
• D.$k > 20$
• E.$7 < k < 20$
• F.all values of $k$

Answer: C

• A.2.1 J
• B.2.8 J
• C.3.5 J
• D.4.2 J
• E.4.9 J
• F.5.6 J

Answer: B