Physics Essay Test 2023

[PAPER 2]
Essay
[60 marks]

Answer eight questions in all: five questions from Part I and three questions from Part II.

PART I
[15 marks]

Answer any five questions from this part.

All questions carry equal marks.

1. A thin aluminium wire is gradually stretched until it breaks. Sketch a force-extension graph for the wire and on the graph indicate the:

(a) Elastic limit;

(b) Maximum load.

[4 marks]

2. (a) State one disadvantage of fibre optic cables as compared to copper cables in the telecommunication industry.

(b) Name two applications of fibre optics in the medical field.

[3 marks]

3. (a) What are ferromagnetic materials?

(b) Name two elements in the periodic table that are ferromagnetic.

[3 marks]

4. The mutual force, F, between two bodies, their distance apart, r, and the product of their masses, m, are related to the universal gravitational constant, G, by the formula:

$$F = \frac{Gm}{r^2}$$

Show that the formula is dimensionally correct.

[3 marks]

5. State the effect of each of the following factors on the rate of diffusion of a fluid:

(a) Temperature;

(b) Concentration gradient;

(c) Density of the fluid.

[3 marks]

6. (a) What is a projectile?

(b) What is a trajectory?

[3 marks]

7. (a) Explain the wave-particle duality of matter.

(b) Name one phenomenon that demonstrates that light behaves as a:

(i) wave;

(ii) particle.

[3 marks]

PART II
[45 marks]

Answer three questions from this part.
All questions carry equal marks

8. (a) State three characteristics of an elastic collision.

[3 marks]

(b) An object of mass 2 kg moving with a speed, u, collided with a stationary box. After collision, the object continued in its original direction with one-quarter of its initial speed. If the total kinetic energy of the colliding system remains constant, calculate the mass of the box.

[5 marks]

(c) A ball thrown vertically upwards to a height, h, is allowed to fall to the point of projection.
Sketch a:

(i) distance-time graph for the motion;

(ii) displacement-time graph for the motion.

[4 marks]

(d) (i) State two differences between distance and displacement.
(ii) For a given direction, state the relationship between distance and displacement.

[3 marks]

9. (a) State three factors that affect the rate of evaporation.

[3 marks]

(b) A heating coil of resistance, 30 Ω is connected to a 230 V supply for 3 minutes to boil a quantity of water in a container of thermal capacity 150 J K^-1. The initial temperature of the water is 50 °C and its specific heat capacity is 4.2 kJ kg^-1 K^-1. Calculate the quantity of water in the container.

[4 marks]

(c) An insulating vessel contains 80 g of a block of ice at -12 °C. If 450 g of water at 60 °C is added to the ice in the vessel:

(i) Determine whether or not the ice will melt completely;

(ii) Calculate the final temperature of the system.

Given: Specific heat capacity of ice = 2100 J kg^-1 K^-1,
Latent heat of fusion of ice = 3.33 × 10⁵ J kg^-1,
Specific heat capacity of water = 4200 J kg^-1 K^-1

[6 marks]

(d) State two differences between heat transfer by conduction and by convection.

[2 marks]

Answers to Question 9a - d

9. (a) Three factors affecting evaporation:

1. Temperature of the liquid

2. Surface area exposed

3. Air movement (wind) or humidity

(b) Energy supplied by coil:

\[ P = \frac{V^2}{R} \]

\[ P = \frac{230^2}{30} \]

\[ P = 1763.33 \, \text{W} \]

\[ Q = P \times t \]

\[ Q = 1763.33 \times 180 \]

\[ Q = 317400 \, \text{J} \]

Let mass of water be $ m $:

\[ Q = mc\Delta T + C_{\text{container}} \times \Delta T \]

[ 317400 = 4200 × m × 50

+ 150 × 50 ]

\[ 317400 = 210000m + 7500 \]

\[ 309900 = 210000m \]

\[ m = \frac{309900}{210000} \]

\[ m \approx 1.476 \, \text{kg} \]

(c)(i) Heat to warm ice to 0°C:

\[ Q_1 = mc\Delta T \]

\[ Q_1 = 0.08 \times 2100 \times 12 \]

\[ Q_1 = 2016 \, \text{J} \]

Heat to melt ice at 0°C:

\[ Q_2 = mL \]

\[ Q_2 = 0.08 \times 3.33 \times 10^5 \]

\[ Q_2 = 26640 \, \text{J} \]

Total required:

\[ Q_{\text{total}} = 2016 + 26640 \] \[ = 28656 \, \text{J} \]

Energy from warm water:

\[ Q = mc\Delta T \]

\[ Q = 0.45 \times 4200 \times 60 \]

\[ Q = 113400 \, \text{J} \]

Conclusion: Ice will melt completely since available energy is greater than energy required.

(c)(ii) Remaining energy:

\[ Q = 113400 - 28656 \] \[ = 84744 \, \text{J} \]

Total water mass:

\[ m = 0.45 + 0.08 = 0.53 \, \text{kg} \]

Let final temperature be $ T $:

\[ Q = mc\Delta T \]

\[ 84744 = 0.53 \times 4200 \times T \]

\[ 84744 = 2226T \]

\[ T = \frac{84744}{2226} \]

\[ T \approx 38.05^\circ C \]

(d) Differences between conduction and convection:

1. Conduction occurs in solids, convection in fluids (liquids and gases).

2. Conduction transfers heat without movement of particles; convection involves particle movement.

10. (a) Explain briefly how stationary waves are formed.

[2 marks]

(b) A standing wave formed between two points separated by a distance of 6 m is represented by the equation:

\[ y = 0.06 \cos\left(\frac{2\pi x}{3}\right) \sin(100\pi t) \]

where $x$ and $y$ are in metres and $t$ is in seconds.

Determine the:

(i) amplitude of the travelling waves;

(ii) speed of the travelling waves;

(iii) number of loops, $n$, formed between the two points.

[8 marks]

(c) A transparent liquid of refractive index 1.57 is poured into a vessel to a depth of 5 cm. On top of the liquid is a layer of alcohol 10 cm deep. If the refractive index of alcohol is 1.45, determine the apparent displacement of the base of the vessel, when an observer is looking perpendicularly at the surface of the liquid.

[4 marks]

(d) Name one electromagnetic wave that is widely used in medical diagnostics.

[1 mark]

Answers to Question 10 (a) - (d)

10. (a) Stationary waves are formed when two waves of the same frequency and amplitude travel in opposite directions and interfere. This results in points of no displacement (nodes) and points of maximum displacement (antinodes).

(b) Given:

\[ y = 0.06 \cos\left(\frac{2\pi x}{3}\right) \sin(100\pi t) \]

(i) Amplitude of the travelling waves = 0.06 m

(ii) Comparing with standard form:

\[ y = A \cos(kx) \sin(\omega t) \] where $k = \frac{2\pi}{\lambda}$ and $\omega = 2\pi f$

\[ k = \frac{2\pi}{3} \Rightarrow \lambda = 3 \, \text{m} \]

\[ \omega = 100\pi \]

\[ f = \frac{100\pi}{2\pi} = 50 \, \text{Hz} \]

\[ v = f \lambda = 50 \times 3 = 150 \, \text{m/s} \]

Speed of the travelling waves = 150 m/s

(iii) Distance between nodes = $\frac{\lambda}{2} = \frac{3}{2} = 1.5 \, \text{m}$

\[ \frac{6}{1.5} = 4 \, \text{loops} \]

Number of loops, $n = 4$

(c) Apparent depth = $\frac{\text{real depth}}{\text{refractive index}}$

Apparent depth of alcohol layer:

\[ d_1 = \frac{10}{1.45} = 6.90 \, \text{cm} \]

Apparent depth of liquid layer:

\[ d_2 = \frac{5}{1.57} = 3.18 \, \text{cm} \]

Total apparent depth = $6.90 + 3.18 = 10.08 \, \text{cm}$

Real depth = $10 + 5 = 15 \, \text{cm}$

\[ \text{Apparent displacement} \]\[= 15 - 10.08 = 4.92 \, \text{cm} \]

Apparent displacement = 4.92 cm

(d) X-rays

11. (a) (i) What is an electrical circuit?

(ii) List four basic components of any electrical circuit giving an example of each.

[6 marks]

(b)

(i) Define the term relative permittivity.

(ii) A parallel plate capacitor of area $5.0 \times 10^{-2} \, \text{m}^2$ has a plate separation of 2 mm in air. If a material of thickness 1.5 mm and relative permittivity 4.0 fills the gap between the plates, calculate the capacitance of the capacitor.

\[\varepsilon_0 = 8.9 \times 10^{-12} \, \text{F m}^{-1}\]

[6 marks]

(c) In a metre bridge experiment, a student was unable to find the balance point. Give two reasons for the occurrence.

[2 marks]

(d) State one use of the metre bridge circuit.

[1 mark]

Answers to Question 11 (a) - (d)

11. (a) (i) An electrical circuit is a closed path through which electric current flows, consisting of electrical components connected by conductors.

(ii) Four basic components of any electrical circuit and their examples:

Resistor: Limits the flow of current (e.g., carbon resistor)
Capacitor: Stores electrical energy (e.g., ceramic capacitor)
Inductor: Opposes change in current (e.g., coil of wire)
Power source: Provides energy to the circuit (e.g., battery)

(b) (i) Relative permittivity is the ratio of the permittivity of a material to the permittivity of free space. It indicates how much the material can increase the capacitance compared to air.

(ii) Given:

Area, $ A = 5.0 \times 10^{-2} \, \text{m}^2 $
Plate separation, $ d = 2 \, \text{mm} = 2 \times 10^{-3} \, \text{m} $
Material thickness, $ t = 1.5 \, \text{mm} = 1.5 \times 10^{-3} \, \text{m} $
Air gap thickness = $ d - t = 0.5 \times 10^{-3} \, \text{m} $
Relative permittivity, $ \varepsilon_r = 4.0 $
Vacuum permittivity, $ \varepsilon_0 = 8.9 \times 10^{-12} \, \text{F/m} $

Capacitance of a capacitor with two dielectrics in series:

\[ \frac{1}{C} = \frac{d_1}{\varepsilon_0 A} + \frac{d_2}{\varepsilon_r \varepsilon_0 A} \] where:
$ d_1 = 0.5 \times 10^{-3} \, \text{m} $ (air)
$ d_2 = 1.5 \times 10^{-3} \, \text{m} $ (material)

Substituting values:

\[ \frac{1}{C} = \frac{0.5 \times 10^{-3}}{8.9 \times 10^{-12} \times 5.0 \times 10^{-2}} \]\[+ \frac{1.5 \times 10^{-3}}{4 \times 8.9 \times 10^{-12} \times 5.0 \times 10^{-2}} \]

\[ \frac{1}{C} = \frac{0.5 \times 10^{-3}}{4.45 \times 10^{-13}} + \frac{1.5 \times 10^{-3}}{1.78 \times 10^{-12}}\]\[ \Rightarrow \frac{1}{C} = 1.1236 \times 10^{9} + 8.4269 \times 10^{8}\]\[ = 1.9663 \times 10^{9} \]

\[ C = \frac{1}{1.9663 \times 10^9} \]\[= 5.086 \times 10^{-10} \, \text{F} \]\[= \boxed{508.6 \, \text{pF}} \]

(c) Two reasons why a student may be unable to find the balance point in a metre bridge experiment:

Poor electrical contact at the junctions
The resistance of the unknown or known resistor is too high or too low, moving the balance point outside the bridge wire

(d) One use of the metre bridge circuit is to determine an unknown resistance using the principle of a Wheatstone bridge.

12. (a) Distinguish between $\beta$ and $\gamma$ radiations under the following headings:

(i) Nature;

(ii) Charge;

(iii) Speed;

[3 marks]

(b) State two:

(i) Similarities;

(ii) Differences;

between photoelectrons and thermoelectrons.

[4 marks]

(c) A metal, X has a work function of 2.0 eV.

(i) Explain the underlined statement.

(ii) If X is illuminated with light of wavelength $4.5 \times 10^{-7} \, \text{m}$, calculate the:

(A) Cut-off wavelength;

(β) Maximum energy of the liberated electrons;

(γ) Stopping potential.

[$h = 6.6 \times 10^{-34} \, \text{Js}$, $c = 3.0 \times 10^8 \, \text{ms}^{-1}$, $1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J}$, $e = 1.6 \times 10^{-19} \, \text{C}$]

[8 marks]

Answers to Question 12 (a) – (c)

12. (a) Differences between $\beta$ and $\gamma$ radiations:

(i) Nature: $\beta$-radiation consists of fast-moving electrons or positrons, while $\gamma$-radiation is electromagnetic radiation (photons).
(ii) Charge: $\beta$-particles carry a negative (or positive, for positrons) charge; $\gamma$-rays are neutral (no charge).
(iii) Speed: $\beta$-particles travel at speeds less than the speed of light; $\gamma$-rays travel at the speed of light.

(b) Similarities and differences between photoelectrons and thermoelectrons:

(i) Similarities:

Both are electrons emitted from the surface of a metal.
Both involve overcoming the work function of the metal.

(ii) Differences:

Photoelectrons are emitted due to the absorption of photons (light energy).
Thermoelectrons are emitted due to the heating of the metal (thermal energy).

(c) Given:

Work function, \[\phi = 2.0 \, \text{eV}\] \[= 2.0 \times 1.6 \times 10^{-19}\] \[= 3.2 \times 10^{-19} \, \text{J}\]

Wavelength, $\lambda = 4.5 \times 10^{-7} \, \text{m}$

\[h = 6.6 \times 10^{-34} \, \text{Js}, \quad\] \[c = 3.0 \times 10^8 \, \text{m/s}, \quad\] \[e = 1.6 \times 10^{-19} \, \text{C}\]

(i) The work function of 2.0 eV means the minimum energy required to eject an electron from the surface of metal X is 2.0 electron volts.

(ii) Calculations:

(A) Cut-off wavelength, $\lambda_0$:

\[ \phi = \frac{hc}{\lambda_0} \Rightarrow \lambda_0 \]\[= \frac{hc}{\phi} \]

\[ \lambda_0 = \frac{6.6 \times 10^{-34} \times 3.0 \times 10^8}{3.2 \times 10^{-19}} = 6.19 \times 10^{-7} \, \text{m} \]

(β) Maximum energy of liberated electrons, $E_k$:

\[ E = \frac{hc}{\lambda} \]\[= \frac{6.6 \times 10^{-34} \times 3.0 \times 10^8}{4.5 \times 10^{-7}} \]\[= 4.4 \times 10^{-19} \, \text{J} \]

\[ E_k = E - \phi \]\[= 4.4 \times 10^{-19} - 3.2 \times 10^{-19} \]\[= 1.2 \times 10^{-19} \, \text{J} \]

(γ) Stopping potential, $V_s$:

\[ V_s = \frac{E_k}{e} = \frac{1.2 \times 10^{-19}}{1.6 \times 10^{-19}} \]\[= 0.75 \, \text{V} \]

END OF PAPER

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Our advertising practices comply with:

Google AdSense Publisher Policies
Local advertising standards and regulations
Educational content guidelines
Age-appropriate advertising requirements

12.2 Copyright Compliance

We respect intellectual property rights and maintain compliance with copyright laws regarding educational fair use of examination materials.

13. Platform Modifications and Updates

13.1 Content Updates

We regularly update our platform with:

New examination papers as they become available
Improved explanations and study materials
Enhanced user interface and functionality
Updated advertising formats and placements

13.2 Terms Modifications

We reserve the right to modify these Terms of Service to:

Comply with changing advertising policies
Reflect new platform features or content
Address legal or regulatory requirements
Improve user experience and service quality

Updated terms will be posted on this page with revision dates. Continued use after changes constitutes acceptance of updated terms.

14. Governing Law and Jurisdiction

These Terms of Service shall be governed by and construed in accordance with the laws of the Republic of Liberia. Any disputes arising from these terms or platform use shall be subject to the jurisdiction of Liberian courts.

15. Severability

If any provision of these Terms of Service is found to be unenforceable or invalid, that provision shall be limited or eliminated to the minimum extent necessary so that the remaining terms remain in full force and effect.

16. Entire Agreement

These Terms of Service, together with our Privacy Policy, constitute the entire agreement between you and StudyWASSCE regarding platform use and supersede all prior agreements or understandings.

17. Contact Information

For questions about these Terms of Service, content issues, or platform feedback, please contact us through:

WhatsApp: +231-770450825
Email: davidlamine96@gmail.com
Facebook: @Study For WASSCE
Response Time: We aim to respond within 48-72 hours

For Urgent Issues: Technical problems affecting site access, inappropriate advertisements, or content errors.

For Partnership Inquiries: Educational institutions, content contributors, or collaboration opportunities.

Thank you for using StudyWASSCE! Your use of our platform helps us continue providing free educational resources to students across West Africa. We appreciate your support through advertisement viewing and ethical use of our content.

Physics

Other Subjects

Answer to Question 1a - b

Answers to Question 2a - b

Answers to Question 3a - b

Answer to Question 4

Answers to Question 5a - c

Answers to Question 6a - b

Answers to Question 7a - b

Answers to Question 8a - d

Answers to Question 9a - d

Answers to Question 10 (a) - (d)

Answers to Question 11 (a) - (d)

Answers to Question 12 (a) – (c)

END OF PAPER

About StudyWASSCE

Our Story

The Creator Behind StudyWASSCE

My Journey:

What Makes StudyWASSCE Different

Completely Free Access

Verified and Reliable Content

Student-Focused Design

Our Specialized Focus

Supporting Free Education

How We Stay Free

Our Commitment to Privacy

Impact and Reach

Looking Forward

Continuous Development

Educational Partnerships

Contact the Creator

A Personal Note

Privacy Policy

1. Who We Are

2. Information We Collect

2.1 Automatically Collected Data

2.2 Cookies and Tracking Technologies

3. How We Use Your Information

4. Advertising and Third-Party Services

4.1 Google AdSense

4.2 Google Analytics

5. Data Sharing

6. Consent and Your Choices

7. Data Security

8. Children's Privacy

9. International Users

10. Changes to This Policy

11. Contact Information

Terms of Service

1. About StudyWASSCE

1.1 Who We Are

1.2 Our Content

2. Acceptance of Terms

3. Free Educational Service

3.1 No Cost Access

3.2 Revenue Model

4. Advertising and Cookies Policy

4.1 Advertisement Display

4.2 Google AdSense Compliance

4.3 Cookie Usage

5. Content Usage and Intellectual Property

5.1 Educational Use License

5.2 Prohibited Uses

5.3 Original Compilation Rights

6. Data Collection and Analytics

6.1 Google Analytics

6.2 Purpose of Data Collection

7. User Responsibilities

7.1 Appropriate Use

7.2 Age Requirements

8. Content Accuracy and Educational Disclaimers

8.1 Best Effort Accuracy

8.2 Educational Supplement

9. Platform Availability and Technical Issues

9.1 Service Availability

9.2 Maintenance and Updates

10. Privacy and Data Protection

10.1 Privacy Commitment

10.2 Third-Party Services