ENGAA 2020 D564/32

• A.1.5 cm
• B.2.0 cm
• C.3.0 cm
• D.4.0 cm
• E.4.5 cm

Answer: E

• A.$\frac{\pi}{2160}\,\Omega$
• B.$\frac{\pi}{180}\,\Omega$
• C.$\frac{\pi}{15}\,\Omega$
• D.$\frac{15}{\pi}\,\Omega$
• E.$\frac{180}{\pi}\,\Omega$
• F.$\frac{2160}{\pi}\,\Omega$

Answer: D

A ray of light is directed into a semicircular transparent block, entering at P. The direction of the ray is adjusted until it strikes the centre of the flat face XY of the block at the critical angle and reflects to Q as shown.

The length of XY is $L$.

The speed of light in air is $c$.

What is the time taken by the light to travel from P to Q in the block?

• A.$\frac{L\sqrt{3}}{2c}$
• B.$\frac{L}{c}$
• C.$\frac{2L}{c\sqrt{3}}$
• D.$\frac{L\sqrt{3}}{c}$
• E.$\frac{2L}{c}$
• F.$\frac{4L}{c\sqrt{3}}$

Answer: C

• A.$40\,\text{Nm}^{-1}$
• B.$80\,\text{Nm}^{-1}$
• C.$400\,\text{Nm}^{-1}$
• D.$800\,\text{Nm}^{-1}$
• E.$4000\,\text{Nm}^{-1}$
• F.$8000\,\text{Nm}^{-1}$

Answer: E

A projectile is fired upwards from the ground at an angle of $60^\circ$ to the vertical at a speed of $20\,\text{ms}^{-1}$.

It travels a horizontal distance $d$ and lands with a downwards vertical component of velocity of $4.0\,\text{ms}^{-1}$ on ground that is height $h$ above the starting point of the projectile.

What are $d$ and $h$?

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

• A.$d/\text{m} = 6.0\sqrt{3}$, $h/\text{m} = 4.2$
• B.$d/\text{m} = 6.0\sqrt{3}$, $h/\text{m} = 5.8$
• C.$d/\text{m} = 10\sqrt{3} - 4.0$, $h/\text{m} = 4.2$
• D.$d/\text{m} = 10\sqrt{3} - 4.0$, $h/\text{m} = 14.2$
• E.$d/\text{m} = 10\sqrt{3} + 4.0$, $h/\text{m} = 5.8$
• F.$d/\text{m} = 10\sqrt{3} + 4.0$, $h/\text{m} = 14.2$
• G.$d/\text{m} = 14\sqrt{3}$, $h/\text{m} = 4.2$
• H.$d/\text{m} = 14\sqrt{3}$, $h/\text{m} = 5.8$

Answer: G

Diagram 1 shows the positions of nine equally spaced particles in a medium.

Diagram 2 shows the positions of the same nine particles, at a particular time, while a longitudinal wave is travelling through the medium.

What is the amplitude of the wave?

• A.0.4 m
• B.0.5 m
• C.0.6 m
• D.0.7 m
• E.2.0 m
• F.4.0 m
• G.6.0 m
• H.8.0 m

Answer: D

• A.$9.5 \times 10^{10}\,\text{W}$
• B.$1.8 \times 10^{11}\,\text{W}$
• C.$2.2 \times 10^{11}\,\text{W}$
• D.$3.2 \times 10^{11}\,\text{W}$
• E.$3.6 \times 10^{11}\,\text{W}$
• F.$7.2 \times 10^{11}\,\text{W}$

Answer: B

The diagram shows a solid triangular prism.

The sides of the triangular cross section of the prism are of length $x$.

The height of the prism is $3x$.

The uniform density of the prism is $\rho$.

The gravitational field strength is $g$.

What is the minimum pressure the prism can exert when it rests on level ground?

• A.$3\rho g$
• B.$3\rho gx$
• C.$\frac{\rho g}{4}$
• D.$\frac{\rho gx}{4}$
• E.$\frac{\sqrt{3}\rho g}{4}$
• F.$\frac{\sqrt{3}\rho gx}{4}$

Answer: F

• A.$\frac{5}{9}$
• B.$\frac{4}{5}$
• C.$\frac{5}{6}$
• D.$\frac{6}{5}$
• E.$\frac{5}{4}$
• F.$\frac{9}{5}$

Answer: F

• A.75 N
• B.350 N
• C.500 N
• D.$(425\sqrt{3} - 75)\,\text{N}$
• E.775 N
• F.$(425\sqrt{3} + 75)\,\text{N}$
• G.925 N

Answer: C

• A.$2.0\,\Omega$ and $4.0\,\Omega$
• B.$2.0\,\Omega$ and $9.0\,\Omega$
• C.$4.0\,\Omega$ and $12\,\Omega$
• D.$4.0\,\Omega$ and $36\,\Omega$
• E.$36\,\Omega$ and $162\,\Omega$
• F.$81\,\Omega$ and $162\,\Omega$

Answer: D

• A.$8.0\,\text{k}\Omega$
• B.$12\,\text{k}\Omega$
• C.$16\,\text{k}\Omega$
• D.$20\,\text{k}\Omega$
• E.$32\,\text{k}\Omega$
• F.$36\,\text{k}\Omega$

Answer: D

An elastic cord with spring constant $k$ is fixed to two points P and Q on the diameter of a ring so that the cord is taut but unstretched. The radius of the ring is $r$.

The midpoint of the cord is then pulled and fixed to a point on the ring halfway between P and Q.

What is the energy stored in the elastic cord?

• A.$\frac{1}{2}kr^2$
• B.$2kr^2$
• C.$\frac{1}{2}(\sqrt{2}-1)kr^2$
• D.$2(\sqrt{2}-1)kr^2$
• E.$\frac{1}{2}(3-2\sqrt{2})kr^2$
• F.$2(3-2\sqrt{2})kr^2$

Answer: F

• A.$T(X + \frac{2}{3}Y\sqrt{T})$
• B.$T(X + Y\sqrt{T})$
• C.$\frac{T}{M}(X + \frac{2}{3}Y\sqrt{T})$
• D.$\frac{T}{M}(X + Y\sqrt{T})$
• E.$\frac{Y}{2\sqrt{T}}$
• F.$\frac{Y}{2M\sqrt{T}}$

Answer: A

• A.12 J
• B.24 J
• C.78 J
• D.270 J
• E.840 J
• F.864 J
• G.936 J

Answer: E

The diagram shows a ray of light passing through three mediums, P, Q and R. The boundaries between the three mediums are parallel.

[diagram not to scale]

The ratio of the speed of light in medium P to the speed of light in medium Q is $2 : \sqrt{5}$

The ratio of the speed of light in medium Q to the speed of light in medium R is $3 : \sqrt{6}$

What is the value of $\sin\theta$?

• A.$\frac{\sqrt{2}}{2}$
• B.$\frac{\sqrt{3}}{2}$
• C.$\frac{\sqrt{3}}{6}$
• D.$\frac{\sqrt{5}}{5}$
• E.$\frac{\sqrt{15}}{5}$
• F.$\frac{\sqrt{15}}{6}$

Answer: E

Water in a wide river flows at a constant speed of $0.50\,\text{ms}^{-1}$. A swimmer swims around a square path of side $30\,\text{m}$ marked out by 4 posts R, S, T and U which are fixed to the river bed, as shown.

The swimmer has a constant speed of $1.0\,\text{ms}^{-1}$ relative to the water.

How long does it take for the swimmer to swim around the square path once?

• A.$(60 + 24\sqrt{5})\,\text{s}$
• B.$(60 + 40\sqrt{3})\,\text{s}$
• C.$(80 + 24\sqrt{5})\,\text{s}$
• D.$(80 + 40\sqrt{3})\,\text{s}$
• E.120 s
• F.140 s

Answer: D

The stress in a steel cable increases with time and is then maintained at a constant value, as shown. The wire does not reach its limit of proportionality.

The table shows properties of the steel used in the cable and the dimensions of the cable.

How much work was done to stretch the cable?

• A.320 J
• B.1.28 kJ
• C.2.56 kJ
• D.320 kJ
• E.640 kJ
• F.1.60 MJ
• G.6.40 MJ

Answer: B

The following graph shows how the displacement of an object travelling along a straight, horizontal track varies with time.

Which graph shows the velocity of this object against displacement?

• A.Graph A
• B.Graph B
• C.Graph C
• D.Graph D
• E.Graph E
• F.Graph F
• G.Graph G
• H.Graph H

Answer: C

• A.$3\left(\frac{kE^2}{2}\right)^{\frac{1}{3}}$
• B.$3\left(\frac{kE^2}{4}\right)^{\frac{1}{3}}$
• C.$3\left(\frac{kE^2}{9}\right)^{\frac{1}{3}}$
• D.$3\left(\frac{kE^2}{16}\right)^{\frac{1}{3}}$
• E.$(2kE^2)^{\frac{1}{3}}$
• F.$(4kE^2)^{\frac{1}{3}}$
• G.$(9kE^2)^{\frac{1}{3}}$
• H.$(16kE^2)^{\frac{1}{3}}$

Answer: D