ENGAA 2019 D564/12

The ray diagram shows light passing from a vacuum into a medium.

Two angles, $x$ and $y$, are shown on the diagram.

When $x$ is $60^\circ$, $y$ is $45^\circ$.

When $x$ is $45^\circ$, what is the value of $\sin y$?

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

Answer: A

Identical resistors are used to produce three different arrangements X, Y and Z.

Each arrangement is connected, in turn, across the same battery which has a negligible internal resistance.

The total power developed in each of the arrangements is determined.

What is the order of the arrangements when placed in order of increasing power?

• A.X, Y, Z
• B.X, Z, Y
• C.Y, X, Z
• D.Y, Z, X
• E.Z, X, Y
• F.Z, Y, X

Answer: A

A block of mass 2.0 kg is on a plane which is inclined to the horizontal at an angle of $30^\circ$.

The block is attached to a load of mass $M$ by a light, inextensible string which passes over a smooth pulley.

The load moves downwards at a constant speed.

A constant friction force of 5.0 N acts on the block while it moves.

What is the value of $M$?

(gravitational field strength = $10\,\text{Nkg}^{-1}$; assume that air resistance is negligible)

• A.0.50 kg
• B.1.0 kg
• C.1.5 kg
• D.2.5 kg
• E.4.0 kg
• F.6.0 kg

Answer: C

The battery in the circuit shown has an emf of 16 V and an internal resistance of $1.0\,\Omega$.

Which line in the table gives the voltmeter readings when switch S is in its open and closed states?

• A.voltmeter reading / V when S is open: 4.0, when S is closed: 2.0
• B.voltmeter reading / V when S is open: 4.0, when S is closed: 6.0
• C.voltmeter reading / V when S is open: 4.0, when S is closed: 2.4
• D.voltmeter reading / V when S is open: 6.0, when S is closed: 2.4
• E.voltmeter reading / V when S is open: 6.0, when S is closed: 4.0
• F.voltmeter reading / V when S is open: $\frac{48}{11}$, when S is closed: $\frac{48}{19}$
• G.voltmeter reading / V when S is open: $\frac{48}{11}$, when S is closed: $\frac{48}{7.0}$
• H.voltmeter reading / V when S is open: $\frac{128}{11}$, when S is closed: $\frac{64}{7.0}$

Answer: B

• A.0 m
• B.72 m
• C.144 m
• D.192 m
• E.288 m
• F.576 m

Answer: E

• A.$\frac{v_{\text{air}} \times \cos 65^\circ}{f}$
• B.$\frac{v_{\text{air}} \times \sin 65^\circ}{f}$
• C.$\frac{f}{v_{\text{air}} \times \cos 65^\circ}$
• D.$\frac{f}{v_{\text{air}} \times \sin 65^\circ}$
• E.$\frac{v_{\text{air}}}{f \times \cos 65^\circ}$
• F.$\frac{v_{\text{air}}}{f \times \sin 65^\circ}$
• G.$\frac{f \times \cos 65^\circ}{v_{\text{air}}}$
• H.$\frac{f \times \sin 65^\circ}{v_{\text{air}}}$

Answer: A

• A.98 kPa
• B.108 kPa
• C.198 kPa
• D.980 kPa
• E.1080 kPa
• F.2940 kPa
• G.3040 kPa

Answer: E

• A.$R \left( \frac{h\rho g - P}{x\rho g - P} \right)^{\frac{1}{3}}$
• B.$R \left( \frac{h}{x} \right)^{\frac{1}{3}}$
• C.$R \left( \frac{h\rho g + P}{x\rho g + P} \right)^{\frac{1}{3}}$
• D.$R \left( \frac{x\rho g - P}{h\rho g - P} \right)^{\frac{1}{3}}$
• E.$R \left( \frac{x}{h} \right)^{\frac{1}{3}}$
• F.$R \left( \frac{x\rho g + P}{h\rho g + P} \right)^{\frac{1}{3}}$

Answer: C

• A.2.0 N
• B.6.0 N
• C.10 N
• D.12 N
• E.16 N
• F.$10\sqrt{3}$ N
• G.26 N
• H.$(16 + 10\sqrt{3})$ N

Answer: G

A non-uniform beam PQ of length 5.0 m and weight $X$ rests on a pivot placed 3.0 m from end P. It is kept in equilibrium in a horizontal position by an upward force of magnitude $0.60X$ acting at end P.

The normal contact force at the pivot is 800 N.

What is the weight of the beam and how far is the centre of gravity of the beam from the pivot?

• A.weight of beam: 500 N, distance from pivot: 0.50 m
• B.weight of beam: 500 N, distance from pivot: 1.8 m
• C.weight of beam: 500 N, distance from pivot: 3.0 m
• D.weight of beam: 2000 N, distance from pivot: 0.50 m
• E.weight of beam: 2000 N, distance from pivot: 1.8 m
• F.weight of beam: 2000 N, distance from pivot: 3.0 m

Answer: E

• A.$2.20\,\text{ms}^{-1}$
• B.$4.50\,\text{ms}^{-1}$
• C.$6.70\,\text{ms}^{-1}$
• D.$7.80\,\text{ms}^{-1}$
• E.$13.3\,\text{ms}^{-1}$
• F.$37.2\,\text{ms}^{-1}$

Answer: C

• A.0.010 W
• B.0.020 W
• C.0.040 W
• D.0.080 W
• E.1.0 W
• F.2.0 W
• G.4.0 W
• H.8.0 W

Answer: A

The circuit below contains three identical resistors, and two identical cells. When the switch is open, the power dissipated by resistor X is $P$.

What is the power dissipated by resistor X after the switch is closed?

• A.$\frac{P}{4}$
• B.$\frac{9P}{16}$
• C.$\frac{3P}{4}$
• D.$P$
• E.$\frac{16P}{9}$
• F.$\frac{9P}{4}$

Answer: B

• A.$\frac{Mal}{EA}$
• B.$\frac{Ma}{EA}$
• C.$\frac{(Ma + D_2)l}{EA}$
• D.$\frac{Ma + D_2}{EA}$
• E.$\frac{(Ma + ma + D_1 + D_2)l}{EA}$
• F.$\frac{Ma + ma + D_1 + D_2}{EA}$

Answer: C

Four resistors, P, Q, R and S, are connected to a battery with negligible internal resistance, as shown in the diagram.

P and S each have resistance $x$. Q and R each have resistance $2x$.

A fifth resistor, T, which has resistance $x$, is to be added to the circuit in one of the following listed positions, as shown in the diagram:

1 in parallel with P
2 in series with Q
3 in parallel with R

Which of the positions for resistor T causes an increase in the magnitude of the voltmeter reading?

• 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: E

A ball is thrown vertically upwards in air. The ball travels upwards to reach its highest point and then falls back down to its initial starting position. The velocity-time graph for the ball is shown.

Which of the following statements is/are correct?

1 The magnitude of the acceleration of the ball is only equal to the magnitude of the acceleration of free fall when it is at its highest point.

2 The time taken for the upward journey of the ball is equal to the time taken for the journey back down to its starting position.

3 The maximum increase in the gravitational potential energy of the ball is less than its initial kinetic energy and greater than its kinetic energy when it returns to its starting position.

• 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: F

• A.1.0 m
• B.1.6 m
• C.2.0 m
• D.3.0 m
• E.3.2 m
• F.6.0 m
• G.7.0 m
• H.11 m

Answer: A

A drawbridge system consists of a uniform ramp, of weight $W$, that is smoothly hinged at its lower end. The upper end is connected by a light, inextensible cable to a winch that is fixed to the wall in the position shown in the diagram.

The ramp is lowered slowly, at constant speed, from its closed (vertical) position ($\theta = 0^\circ$) to its open (horizontal) position ($\theta = 90^\circ$).

What is the maximum tension in the cable during this process?

(double-angle identities: $\sin 2\theta = 2\sin\theta \cos\theta$; $\cos 2\theta = \cos^2 \theta - \sin^2 \theta$)

• A.$\frac{W}{2}$
• B.$\frac{W}{\sqrt{2}}$
• C.$\frac{\sqrt{3}W}{2}$
• D.$W$
• E.$\frac{2W}{\sqrt{3}}$
• F.$\sqrt{2}W$
• G.$2W$

Answer: B

• A.0
• B.$\frac{ME}{(M + m)}$
• C.$\frac{mE}{(M+m)}$
• D.$\frac{(M+m)E}{m}$
• E.$\frac{(M+m)E}{M}$
• F.$\frac{mME}{(M+m)^2}$
• G.$E$

Answer: B

The critical angle for light incident on a boundary from medium X to air is $45^\circ$.

The critical angle for light of the same frequency incident on a boundary from medium Y to air is $60^\circ$.

There is a boundary between medium X and medium Y. Light of the same frequency travelling in one of these mediums is incident on this boundary.

In which direction of incidence is there a critical angle at this boundary, and within what range is this critical angle?

• A.direction of incidence: X to Y, critical angle: between $0^\circ$ and $30^\circ$
• B.direction of incidence: X to Y, critical angle: between $30^\circ$ and $45^\circ$
• C.direction of incidence: X to Y, critical angle: between $45^\circ$ and $60^\circ$
• D.direction of incidence: X to Y, critical angle: between $60^\circ$ and $90^\circ$
• E.direction of incidence: Y to X, critical angle: between $0^\circ$ and $30^\circ$
• F.direction of incidence: Y to X, critical angle: between $30^\circ$ and $45^\circ$
• G.direction of incidence: Y to X, critical angle: between $45^\circ$ and $60^\circ$
• H.direction of incidence: Y to X, critical angle: between $60^\circ$ and $90^\circ$

Answer: C