ENGAA 2021 (Paper 2)

• A.$\frac{1}{125x^7y^2}$
• B.$\frac{1}{125x^6y^2}$
• C.$\frac{1}{25x^6y}$
• D.$\frac{1}{25x^4y}$
• E.$\frac{1}{5x^3}$
• F.$\frac{1}{5x^2}$
• G.$\frac{y}{x^2}$
• H.$5xy^2$

Answer: E

Air is trapped in a cylinder by a piston. The density of the air in the cylinder is $\rho$.

The piston is moved so that the pressure of the trapped air increases by 20%. The temperature of the trapped air does not change.

What is the new density of the trapped air?

(Assume that air is an ideal gas.)

• A.$0.69\rho$
• B.$0.80\rho$
• C.$0.83\rho$
• D.$1.00\rho$
• E.$1.20\rho$
• F.$1.44\rho$

Answer: E

• A.$q = \frac{2r}{24-3pr}$
• B.$q = \frac{3r}{2r-p}$
• C.$q = \frac{6r}{4-p}$
• D.$q = \frac{6r}{8-pr}$
• E.$q = \frac{r-2}{12p}$
• F.$q = \frac{3r-6}{4p}$
• G.$q = \frac{pr-8}{12p}$
• H.$q = \frac{3pr-24}{4p}$

Answer: D

• A.20%
• B.25%
• C.31%
• D.69%
• E.75%
• F.80%
• G.91%
• H.100%

Answer: F

Two solid cylinders, P and Q, are shown, where $x > y$.

Cylinder P has diameter x and height y.

Cylinder Q has diameter y and height x.

What is the positive difference between the total surface areas of P and Q?

• A.0
• B.$\frac{\pi}{4}(x^2 - y^2)$
• C.$\frac{\pi}{2}(x^2 - y^2)$
• D.$\pi(x^2 - y^2)$
• E.$2\pi(x^2 - y^2)$
• F.$\frac{\pi}{4}xy(x-y)$
• G.$\pi xy(x-y)$

Answer: C

A light spring has an uncompressed length of 0.10 m. When an object of mass 0.5 kg rests in equilibrium on top of the spring, the length of the spring reduces to 0.08 m as shown.

What is the energy stored in the spring due to the compression?

(gravitational field strength = $10 N kg^{-1}$; the spring obeys Hooke's law)

• A.0.005 J
• B.0.02 J
• C.0.05 J
• D.0.1 J
• E.0.2 J
• F.0.4 J

Answer: C

• A.item P final price: lower than original, item Q final price: lower than original
• B.item P final price: lower than original, item Q final price: higher than original
• C.item P final price: higher than original, item Q final price: lower than original
• D.item P final price: higher than original, item Q final price: higher than original
• E.item P final price: the same as original, item Q final price: the same as original

Answer: A

• A.$(\frac{19}{20})^2 P$
• B.$(\frac{19}{20}) P$
• C.P
• D.$(\frac{20}{19}) P$
• E.$(\frac{20}{19})^2 P$

Answer: D

[diagram not to scale]

SQT is a right-angled triangle with the right angle at Q.

The point R is on SQ such that SR : RQ = 1:3

QRP is a right-angled triangle with the right angle at Q.

PR = ST = 8 cm

QT = 4 cm

What is the length of PQ, in cm?

• A.$2\sqrt{3}$
• B.$4\sqrt{3}$
• C.$\sqrt{19}$
• D.$\sqrt{37}$
• E.$\sqrt{55}$
• F.$\sqrt{61}$

Answer: D

A train accelerates from rest along a straight, horizontal section of track.

The force exerted on the train due to its motors is constant and there is a constant friction force of $1.8 \times 10^7$ N.

The graph shows how the momentum of the train changes with time.

What is the force exerted on the train due to its motors?

• A.$3.0 \times 10^6$ N
• B.$6.0 \times 10^6$ N
• C.$1.2 \times 10^7$ N
• D.$1.5 \times 10^7$ N
• E.$2.1 \times 10^7$ N
• F.$2.4 \times 10^7$ N
• G.$3.0 \times 10^7$ N
• H.$4.2 \times 10^7$ N

Answer: E

• A.-43
• B.-12
• C.-2
• D.0
• E.2
• F.12
• G.43

Answer: F

• A.$\frac{3}{8}$ m
• B.$\frac{5}{8}$ m
• C.1.0 m
• D.$\frac{11}{8}$ m
• E.24 m
• F.40 m
• G.64 m
• H.88 m

Answer: H

• A.$-\frac{\sqrt{3}}{9}$
• B.$-5\sqrt{2} + 10$
• C.$3\sqrt{3} - 8$
• D.$6\sqrt{3} - 10$
• E.$14\sqrt{2} - 20$
• F.$15\sqrt{3} - 26$
• G.$21\sqrt{3} - 38$

Answer: F

A 6.0 V battery is connected to an 8.0 $\Omega$ resistor and a filament lamp as shown in the circuit diagram.

The reading on the ammeter is 0.25 A.

Which graph is a possible V-I graph for the filament lamp?

• A.Graph labeled A
• B.Graph labeled B
• C.Graph labeled C
• D.Graph labeled D
• E.Graph labeled E
• F.Graph labeled F

Answer: B

• A.$\frac{2}{27}$
• B.$\frac{1}{12}$
• C.$\frac{1}{9}$
• D.$\frac{4}{27}$
• E.$\frac{1}{6}$
• F.$\frac{1}{4}$
• G.$\frac{7}{12}$

Answer: B

• A.$\frac{1}{4}$
• B.$\frac{17}{20}$
• C.$\frac{31}{28}$
• D.$\frac{6}{5}$
• E.$\frac{5}{4}$
• F.2

Answer: C

The greatest diagonal distance between the two vertices of a cuboid, as shown in the diagram, is $\sqrt{77}$ cm.

A similar cuboid has all its lengths exactly half the lengths of the original cuboid.

The sides of this smaller cuboid are 2 cm, 3 cm and x cm.

What is the value of x, in cm?

• A.$\frac{5}{2}$
• B.5
• C.$\frac{5\sqrt{2}}{2}$
• D.$5\sqrt{2}$
• E.$\frac{\sqrt{102}}{2}$
• F.$\sqrt{102}$

Answer: A

• A.2.5 °C
• B.8.3 °C
• C.10.0 °C
• D.15.0 °C
• E.16.7 °C
• F.22.5 °C

Answer: D

• A.$100fmpx$
• B.$\frac{100 fmp}{x}$
• C.$\frac{100mpx}{f}$
• D.$\frac{100mp}{fx}$
• E.$\frac{fmpx}{100}$
• F.$\frac{fmp}{100x}$
• G.$\frac{mpx}{100 f}$
• H.$\frac{mp}{100 fx}$

Answer: H

• A.$\frac{t_1}{t_2} L$
• B.$\frac{t_2}{t_1} L$
• C.$\frac{t_1}{2t_2} L$
• D.$\frac{t_2}{2t_1} L$
• E.$\frac{(t_2 - t_1)}{t_2} L$
• F.$\frac{(t_2 - t_1) L}{2t_2}$

Answer: E

• A.-12
• B.$-\frac{1}{4}$
• C.3
• D.$\frac{63}{16}$
• E.5

Answer: C

• A.$4.5 ms^{-2}$
• B.$6.0 ms^{-2}$
• C.$8.0 ms^{-2}$
• D.$16 ms^{-2}$
• E.$4.5\sqrt{3} ms^{-2}$
• F.$6.0\sqrt{3} ms^{-2}$
• G.$8.0\sqrt{3} ms^{-2}$
• H.$16\sqrt{3} ms^{-2}$

Answer: G

• A.d
• B.2d
• C.2a + d
• D.2a + 2d
• E.2a + nd
• F.2a + 2nd
• G.2a + (2n - 1)d
• H.2a + (4n - 2)d

Answer: G

A sound wave is travelling from left to right in air. The diagram represents the wave at a particular instant, and a distance of 33 cm is labelled.

The speed of sound in air is $330 ms^{-1}$.

What is the frequency of the sound and in which direction has the air at P been displaced from its mean position?

| | frequency of sound / Hz | displacement of air at P |
| :--- | :--- | :--- |
| A | 1000 | to the left |
| B | 2500 | to the left |
| C | 5000 | to the left |
| D | 1000 | to the right |
| E | 2500 | to the right |
| F | 5000 | to the right |

• A.frequency of sound / Hz: 1000, displacement of air at P: to the left
• B.frequency of sound / Hz: 2500, displacement of air at P: to the left
• C.frequency of sound / Hz: 5000, displacement of air at P: to the left
• D.frequency of sound / Hz: 1000, displacement of air at P: to the right
• E.frequency of sound / Hz: 2500, displacement of air at P: to the right
• F.frequency of sound / Hz: 5000, displacement of air at P: to the right

Answer: B

• A.0
• B.1
• C.2
• D.3
• E.4

Answer: D

A resistor R is connected between terminals X and Y in the circuit shown.

The power transferred in the 4.0 $\Omega$ heater is 9.0 W.

What is the resistance of R?

• A.$1.6 \Omega$
• B.$2.0 \Omega$
• C.$2.67 \Omega$
• D.$4.0 \Omega$
• E.$8.0 \Omega$

Answer: D

• A.$\frac{2\pi}{3} - \frac{\sqrt{3}}{2}$
• B.$\frac{2\pi}{3} - \sqrt{3}$
• C.$\frac{\pi}{2} - \frac{1}{2}$
• D.$\frac{\pi}{2} - 1$
• E.$\pi - \frac{1}{2}$
• F.$\pi - 1$
• G.$\frac{4\pi}{3} - \frac{\sqrt{3}}{2}$
• H.$\frac{4\pi}{3} - \sqrt{3}$

Answer: H

A uniform plank of length 5.0 m rests horizontally as shown.

[diagram not to scale]

There is a pivot 1.0 m from one end of the plank.

A cable at an angle of $60^\circ$ to the horizontal supports the plank at the other end so that it is in equilibrium.

The tension in the cable is 75 N.

What is the weight of the plank?

• A.60 N
• B.$60\sqrt{3}$ N
• C.100 N
• D.$100\sqrt{3}$ N
• E.125 N
• F.$125\sqrt{3}$ N

Answer: D

• A.$\frac{\log_{10} 307}{3}$
• B.$\frac{\log_{10} 81}{3}$
• C.$\frac{\log_{10} 6^{12}}{3}$
• D.$\log_{10} 64$
• E.$\log_{10} 72$
• F.$\log_{10} 108$

Answer: E

A lorry accelerates along a straight, horizontal road with uniform acceleration.

Oil droplets from the lorry fall a small distance onto the road at a constant rate. The time interval between successive drips is t.

The diagram shows four successive oil droplets on the road after the lorry has passed.

The distance between the first two of these droplets is x and the distance between the final two is y.

Which expression gives the acceleration of the lorry?

• A.$\frac{y-x}{3t^2}$
• B.$\frac{y-x}{2t^2}$
• C.$\frac{y-x}{t^2}$
• D.$\frac{2(y-x)}{t^2}$
• E.$\frac{y+x}{t^2}$
• F.$\frac{y+x}{3t^2}$

Answer: B

• A.cos 0.5
• B.cos 0.75
• C.cos 1
• D.sin 0.5
• E.sin 0.75
• F.sin 1

Answer: A

• A.Young modulus / Pa: $5.0 \times 10^{-12}$, energy stored / J: 0.018
• B.Young modulus / Pa: $5.0 \times 10^{-12}$, energy stored / J: 0.036
• C.Young modulus / Pa: $2.0 \times 10^{11}$, energy stored / J: 0.018
• D.Young modulus / Pa: $2.0 \times 10^{11}$, energy stored / J: 0.036
• E.Young modulus / Pa: $2.0 \times 10^{14}$, energy stored / J: 18
• F.Young modulus / Pa: $2.0 \times 10^{14}$, energy stored / J: 36

Answer: C

• A.$\frac{3}{5}$
• B.$\frac{31}{25}$
• C.$\frac{23}{5}$
• D.$\frac{28}{5}$
• E.$\frac{67}{8}$

Answer: B

• A.$4.0 ms^{-1}$
• B.$8.0 ms^{-1}$
• C.$12 ms^{-1}$
• D.$16 ms^{-1}$
• E.$20 ms^{-1}$

Answer: D

• A.0
• B.1
• C.2
• D.3
• E.4
• F.5

Answer: C

• A.$\sqrt{2}R$
• B.$2\sqrt{2}R$
• C.$4\sqrt{2}R$
• D.2R
• E.4R
• F.8R
• G.16R

Answer: G

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

Answer: H

• A.22 m
• B.110 m
• C.136 m
• D.140 m
• E.220 m
• F.1100 m
• G.1360 m
• H.1400 m

Answer: D

PQRS is a rectangle.

P and Q lie on the x-axis.

Q and R lie on the line $x = 15$

S lies on the curve $y = \sqrt{x}$

What is the maximum possible area of the rectangle?

• A.$5\sqrt{5}$
• B.$10\sqrt{5}$
• C.50
• D.$25\sqrt{5}$
• E.100
• F.125

Answer: B

• A.0
• B.$\frac{W}{5}$
• C.$\frac{W}{4}$
• D.$\frac{W}{2}$
• E.$\frac{3W}{5}$
• F.$\frac{3W}{4}$
• G.$\frac{4W}{5}$
• H.W

Answer: E