ENGAA 2023 D564/12

• A.$2g$
• B.$\frac{5}{2}g$
• C.$3g$
• D.$(3 - \sqrt{3})g$
• E.$\left(3 - \frac{1}{\sqrt{3}}\right)g$
• F.$\left(3 - \frac{\sqrt{3}}{2}\right)g$
• G.$\left(3 - \frac{2}{\sqrt{3}}\right)g$

Answer: A

• A.0.15 kg
• B.0.40 kg
• C.1.2 kg
• D.2.5 kg
• E.6.7 kg

Answer: D

Two waves P and Q, which superpose, are shown in the diagram in a particular region at time $t = 0$.

Both waves have period $T$ and are moving in the directions shown by the arrows. Wave P has amplitude 2.0 cm and wave Q has amplitude 1.0 cm.

Which diagram represents the resultant wave formed in the same region by waves P and Q at time $t = \frac{T}{2}$?

• A.Image of resultant wave A, peak amplitude 3.0 cm.
• B.Image of resultant wave B, peak amplitude 3.0 cm.
• C.Image of resultant wave C, peak amplitude 1.5 cm.
• D.Image of resultant wave D, peak amplitude 1.5 cm.
• E.Image of resultant wave E, peak amplitude 1.0 cm.
• F.Image of resultant wave F, peak amplitude 1.0 cm.
• G.Image of resultant wave G, straight line

Answer: F

Four identical springs are arranged as shown and suspended from a support.

The mass of the springs, rod and hook are negligible.

A load of weight 8.4 N is attached to the hook at the lower end of the springs and this causes a total extension of the system of 24 mm.

The arrangement is then changed to:

The load of 8.4 N is attached to the bottom of the lower spring.

What is the total extension of the system at equilibrium in the second arrangement?

(The springs obey Hooke's law.)

• A.3 mm
• B.12 mm
• C.16 mm
• D.24 mm
• E.32 mm
• F.48 mm
• G.64 mm

Answer: E

• A.1.6 ms⁻¹
• B.2.4 ms⁻¹
• C.3.2 ms⁻¹
• D.3.8 ms⁻¹
• E.24 ms⁻¹

Answer: C

The variation of the acceleration with time of an object moving in a straight line is shown on the graph.

At time = 0 s the velocity of the object is $8.0 \text{ms}^{-1}$.

What is the maximum velocity of the object between time = 0 s and time = 6 s?

• A.5.0 ms⁻¹
• B.8.0 ms⁻¹
• C.12 ms⁻¹
• D.20 ms⁻¹
• E.32 ms⁻¹
• F.44 ms⁻¹

Answer: D

The diagram shows a circuit that includes a battery with an emf of 18 V and internal resistance $r$.

The three identical resistors in the external circuit each have resistance $R$.

The terminal potential difference across the battery is 16 V.

Which expression gives $R$ in terms of $r$?

• A.$R = \frac{10r}{3}$
• B.$R = \frac{16r}{3}$
• C.$R = 6r$
• D.$R = 12r$
• E.$R = \frac{27r}{2}$
• F.$R = 24r$
• G.$R = \frac{51r}{2}$

Answer: D

Three identical bar magnets, each of mass $m$, and two identical trolleys, X and Y, also each of mass $m$, are arranged with the bar magnets fixed to the trolleys as shown. The trolleys are held at rest a short distance apart on a smooth horizontal track.

The trolleys are released at the same time. They move towards each other and collide.

Find the value of the ratio

$\frac{\text{kinetic\;energy\;of\;X\;immediately\;before\;collision}}{\text{kinetic\;energy\;of\; Y \;immediately\;before\; collision}}$

• A.$\frac{4}{9}$
• B.$\frac{1}{2}$
• C.$\frac{2}{3}$
• D.1
• E.$\frac{3}{2}$
• F.2
• G.$\frac{9}{4}$

Answer: E

A uniform rod XY of length 3.0 m has a weight of 20 N. The rod is supported by two light wires, P and Q, as shown. P and Q are attached 0.50 m from ends X and Y, respectively.

A 40 N load is moved from end X to end Y. The rod remains horizontal at all times.

Which graph shows the variation of the tension $T$ in wire P with the position of the load as it is moved along the rod?

• A.Graph A: T is constant
• B.Graph B: T starts at some value, steps up to a higher constant value, then drops.
• C.Graph C: T is constant, then drops to a lower constant value.
• D.Graph D: T starts at a high constant value, then drops to zero.
• E.Graph E: T decreases linearly from a maximum value at X to a minimum value at Y.
• F.Graph F: T decreases linearly from a maximum value at X to zero at Y.

Answer: F

A pipe of length $L$ open at both ends contains a stationary sound wave with 1 node, as shown in the diagram.

The frequency of the stationary wave in this pipe is $4f$.

A second pipe is open at one end and closed at the other end. A stationary sound wave in this pipe contains one more node than the stationary wave shown in the diagram.

The frequency of the stationary wave in the second pipe is $f$.

The speed of sound is the same in both pipes.

What is the length of the second pipe?

• A.4L
• B.6L
• C.8L
• D.10L
• E.12L

Answer: B

The resistors in the following four circuits are identical.

The cells are identical and have no internal resistance. Each cell can supply the same total amount of energy at a constant voltage before becoming exhausted.

$t_1$, $t_2$, $t_3$ and $t_4$ are the lengths of time after which the cells in circuits 1, 2, 3, 4, respectively, become exhausted.

Which comparison of $t_1$, $t_2$, $t_3$ and $t_4$ is correct?

• A.$t_1 = t_2 < t_3 = t_4$
• B.$t_1 = t_3 < t_2 = t_4$
• C.$t_2 < t_1 = t_4 < t_3$
• D.$t_2 = t_4 < t_1 = t_3$
• E.$t_3 < t_1 = t_4 < t_2$
• F.$t_3 = t_4 < t_1 = t_2$

Answer: C

• A.$k$
• B.$2mk$
• C.$\sqrt{2mkT}$
• D.$\sqrt{\frac{mk}{2T}}$
• E.$\sqrt{\frac{mk}{8T}}$
• F.$\sqrt{\frac{2mk}{T}}$
• G.$\sqrt{\frac{k}{2mT}}$

Answer: D

• A.$\frac{2W}{A}$
• B.$\frac{4W}{A}$
• C.$\frac{5W}{2A}$
• D.$\frac{2W}{3A}$
• E.$\frac{10W}{3A}$
• F.$\frac{20W}{3A}$
• G.$\frac{5W}{6A}$

Answer: E

A triangular ramp with angles to the horizontal of 60° and 30° is placed with its largest face horizontal. A block of mass 1.5 kg and a block of mass $m$ are joined by a light, inextensible string and placed on the ramp as shown.

The string passes over a light, frictionless pulley.

The maximum force of friction between the block of mass 1.5 kg and the surface of the ramp is 3.5 N.

The maximum force of friction between the block of mass $m$ and the surface of the ramp is 5.0 N.

What is the maximum value of $m$ that allows the blocks to remain stationary on the surfaces?

(gravitational field strength = $10 \text{Nkg}^{-1}$)

• A.1.5 kg
• B.1.65 kg
• C.2.35 kg
• D.$\left(\frac{16\sqrt{3}}{15}\right) \text{kg}$
• E.$(0.60 \sqrt{3}) \text{kg}$
• F.$(0.30 + 1.5\sqrt{3}) \text{kg}$
• G.$(1.7 + 1.5\sqrt{3}) \text{kg}$

Answer: G

A sound wave travels through medium J, reaches a boundary, and then travels through medium K as shown. The thickness of each medium is $L$.

The wave travels a distance $q$ in medium J and a distance $y$ in medium K.

The horizontal distance travelled in medium J is $p$. The horizontal distance travelled in medium K is $x$.

The wave travels at speed $v$ in medium J. The graph shows how the speed of the wave varies with time $t$ as it travels distances $q$ and $y$, and that the wave leaves medium K at $t = 2.75$ ms.

What is the value of $\frac{x}{p}$?

• A.$\frac{3}{200}$
• B.$\frac{3}{40}$
• C.$\frac{8}{75}$
• D.$\frac{3}{8}$
• E.$\frac{8}{15}$
• F.$\frac{8}{3}$
• G.$\frac{200}{3}$

Answer: A

• A.2P
• B.4P
• C.8P
• D.16P
• E.32P
• F.64P

Answer: E

A projectile is launched from an inclined plane.

The graphs show the variation of the horizontal and vertical components of the velocity of the projectile with time from when it is launched until it hits the plane at time $T$.

What is the angle of the plane to the horizontal?

(gravitational field strength = $10 \text{Nkg}^{-1}$)

• A.$\tan^{-1}\frac{1}{32}$
• B.$\tan^{-1}\frac{1}{8}$
• C.$\tan^{-1}\frac{1}{4}$
• D.$\tan^{-1}\frac{5}{16}$
• E.$\tan^{-1}\frac{1}{3}$
• F.$\tan^{-1}\frac{4}{3}$

Answer: C

A tennis ball of mass 0.060 kg travels horizontally and strikes a vertical wall at $30 \text{ms}^{-1}$. It leaves the wall in the opposite direction at $20 \text{ms}^{-1}$.

The graph shows how the resultant horizontal force acting on the ball varies with time during this collision.

What is the duration of the collision?

• A.$\frac{1}{200} \text{s}$
• B.$\frac{1}{150} \text{s}$
• C.$\frac{1}{100} \text{s}$
• D.$\frac{1}{40} \text{s}$
• E.$\frac{1}{30} \text{s}$
• F.$\frac{1}{20} \text{s}$

Answer: E

A battery with an emf of 8.0 V and internal resistance $R$ and another battery with an emf of 4.0 V and internal resistance $2.0 \Omega$ are connected to a cell with an emf of 2.0 V and internal resistance $4.0 \Omega$ in the circuit shown.

The current in the 2.0 V cell is 0.50 A in the direction shown in the diagram.

What is the resistance $R$?

• A.1.6 Ω
• B.2.7 Ω
• C.3.2 Ω
• D.8.0 Ω
• E.16 Ω

Answer: D

• A.$\frac{\rho_0 h}{A}$
• B.$\frac{\rho_0 h}{A} (1 - k)$
• C.$\frac{\rho_0 h}{2A} (2 - k)$
• D.$\frac{\rho_0 h}{A} (1 - 3k)$
• E.$\frac{\rho_0 h}{A} \left( 1 - \frac{k}{3} \right)$
• F.$\frac{\rho_0}{A} \left( 1 - \frac{kh}{3} \right)$
• G.$\frac{\rho_0 h^2}{A} \left( \frac{1}{2} - \frac{k}{4} \right)$

Answer: E