Educational Tour: Tanzania Revenue Authority

Understanding Tax Collection and National Development

Introduction to Tax Education

The Tanzania Revenue Authority (TRA) plays a vital role in national development by collecting government revenue through various taxes. Educational tours of TRA regional offices provide students with a unique opportunity to understand the importance of taxation and how it fuels national progress and public services.

Through guided tours and interactive sessions, students learn about the tax collection process, the different types of taxes, and how tax revenue is allocated to fund essential public services. This experience helps demystify taxation and shows students how their future tax contributions will support national development.

Educational Focus: The tours specifically emphasize the importance of tax compliance, types of taxes collected, revenue allocation to public services, and TRA's collaboration with other government agencies to ensure efficient revenue collection.

Educational Benefits for Students

Visiting Tanzania Revenue Authority offices offers students numerous educational benefits that complement their classroom learning in civics, economics, and social studies:

💰

Understanding Taxation Purpose

Students learn why citizens pay taxes and how taxation forms the foundation of government funding for public services and infrastructure.

📊

Tax Types and Systems

Comprehensive understanding of different tax categories including direct and indirect taxes, and how they affect individuals and businesses.

🏫

Revenue Allocation

Learning how tax money is distributed to fund essential services like education, healthcare, infrastructure, and security.

🌍

National Development

Understanding how tax compliance directly contributes to Tanzania's economic growth and sustainable development.

🤝

Inter-agency Collaboration

Learning how TRA works with other government institutions to enhance revenue collection and combat tax evasion.

💼

Career Inspiration

Exposure to tax administration can inspire interest in careers in revenue collection, economics, accounting, and public finance.

Why Citizens Pay Taxes

Taxation is the primary source of government revenue that enables the provision of public goods and services that benefit all citizens. During TRA tours, students learn about the fundamental reasons for taxation:

Social Contract and Public Goods

Taxes represent the social contract between citizens and the government. In exchange for tax payments, the government provides services that individuals cannot efficiently provide for themselves, such as national defense, public roads, and law enforcement.

Wealth Redistribution

Progressive taxation systems help redistribute wealth by requiring higher earners to pay a larger percentage of their income, which funds social programs that support vulnerable populations.

Economic Stabilization

Tax revenue enables government spending during economic downturns, helping to stabilize the economy and maintain employment levels through public works and social programs.

Key Insight: Taxation is not merely about collecting money but about building a society where collective resources fund shared needs and opportunities for all citizens.

Types of Taxes in Tanzania

Tanzania's tax system includes various types of taxes designed to collect revenue efficiently while maintaining fairness. Students learn about these different tax categories:

👤

Income Tax

Tax on individual and corporate income, including Pay As You Earn (PAYE) for employees and corporate tax for businesses.

🛒

Value Added Tax (VAT)

Consumption tax applied to the price of goods and services at each stage of production and distribution.

📦

Import and Export Duties

Taxes on goods crossing Tanzania's borders, including customs duties and excise taxes on specific imported products.

🏢

Excise Duty

Taxes on specific goods produced domestically, such as alcohol, tobacco, and petroleum products.

🏠

Property Tax

Taxes on property ownership, including land and buildings, collected by local government authorities.

🎯

Withholding Tax

Tax deducted at source from payments like dividends, interest, and royalties before the recipient receives the payment.

Where Tax Money Goes: Funding National Development

One of the most important lessons from TRA tours is understanding how tax revenue is allocated to fund essential public services and infrastructure projects:

🏫

Education

Funding for public schools, teachers' salaries, educational materials, and university subsidies to ensure quality education for all Tanzanian children.

🏥

Healthcare

Support for public hospitals, clinics, medical supplies, and health insurance programs to improve healthcare accessibility and quality.

🛣️

Infrastructure

Construction and maintenance of roads, bridges, railways, and public transportation systems to connect communities and boost economic activity.

🚓

Security

Funding for police services, defense forces, and judicial systems to maintain law, order, and national security.

Additional Public Services Funded by Taxes:

• Social Services: Welfare programs, elderly care, and support for vulnerable populations
• Agricultural Development: Subsidies, research, and extension services for farmers
• Water and Sanitation: Clean water projects and sanitation infrastructure
• Energy Sector: Electricity generation and distribution infrastructure
• Environmental Protection: Conservation efforts and pollution control measures

Tax Compliance and National Development

Tax compliance—the willingness of individuals and businesses to pay their taxes correctly and on time—is crucial for national development. During TRA tours, students learn how tax compliance directly impacts Tanzania's progress:

Benefits of Tax Compliance:

• Predictable Revenue: Enables government to plan and implement long-term development projects
• Improved Public Services: More revenue means better schools, hospitals, and infrastructure
• Economic Stability: Consistent funding for government operations and social programs
• Reduced Borrowing: Lower need for government debt, reducing future tax burdens
• Fairness: Ensures all citizens and businesses contribute their fair share

The Tax Collection Process:

Registration

Taxpayers register with TRA and receive Tax Identification Numbers (TIN)

Declaration

Taxpayers file returns declaring their income or transactions

Assessment

TRA assesses the tax liability based on declarations

Payment

Taxpayers pay their assessed taxes through various channels

Allocation

Revenue is allocated to fund government services and projects

TRA Collaboration with Other Government Agencies

The Tanzania Revenue Authority works closely with various government institutions to enhance tax collection, ensure compliance, and streamline government operations:

Bank of Tanzania

Collaboration on economic data sharing, foreign exchange monitoring, and implementation of monetary policies that affect revenue collection.

Ministry of Finance

Working together on budget preparation, tax policy development, and revenue forecasting to align tax collection with national budgetary needs.

Local Government Authorities

Partnership in property tax collection, business licensing, and sharing of taxpayer information to enhance local revenue collection.

Immigration Department

Cooperation in monitoring cross-border transactions and preventing tax evasion through international movements.

Business Registration & Licensing Agency (BRELA)

Integration of business registration with tax registration to ensure all businesses are properly documented for taxation.

Preventive Services

Joint operations with customs and border control agencies to combat smuggling and ensure proper collection of import duties.

Benefits of Inter-agency Collaboration:

• Improved Efficiency: Streamlined processes reduce duplication and lower compliance costs
• Enhanced Compliance: Better data sharing helps identify tax evaders and ensure fair taxation
• Comprehensive Planning: Coordinated approach to revenue collection and economic planning
• Reduced Fraud: Joint efforts to detect and prevent tax-related crimes and fraud

Tour Information and Educational Activities

Student tours of Tanzania Revenue Authority regional offices are carefully structured to provide maximum educational value while maintaining operational efficiency:

Typical Tour Structure:

• Orientation Session: Introduction to TRA's mission, functions, and importance of taxation
• Department Visits: Tour of various TRA departments including customer service, tax processing, and compliance units
• Interactive Workshops: Hands-on activities demonstrating tax calculation and compliance processes
• Technology Demonstration: Viewing electronic tax systems and online payment platforms
• Q&A Session: Opportunity to ask questions to TRA officials and tax experts

Tour Educational Highlights:

💰

Understanding the social contract of taxation

📊

Learning about different tax types and their purposes

🏫

Seeing how tax money funds public services

🤝

Understanding inter-agency collaboration

💡

Learning about tax compliance benefits

🌍

Connecting tax payments to national development

Conclusion: Building a Tax-Compliant Generation

Educational tours of the Tanzania Revenue Authority provide students with invaluable insights into the importance of taxation and its direct connection to national development. These experiences transform the abstract concept of taxation into tangible understanding, helping students appreciate how their future tax contributions will build a better Tanzania.

By learning about tax types, revenue allocation, and the collaborative nature of government revenue collection, students develop a deeper appreciation for their role as future taxpayers. This knowledge empowers them to become responsible citizens who understand that tax compliance is not just a legal obligation but a civic duty that fuels national progress.

Long-term Impact: Beyond immediate educational benefits, TRA tours can inspire future tax professionals, create greater public understanding of taxation, and contribute to building a culture of voluntary tax compliance in the next generation of Tanzanian citizens.

Disclaimer: This educational resource provides general information about student tours of Tanzania Revenue Authority offices. Specific tour arrangements must be coordinated with TRA regional offices and are subject to operational requirements.

© 2023 Educational Resources - Tanzania Revenue Authority Tours

STUDENT TOUR: Bank of Tanzania

Educational Tour: Bank of Tanzania

Discover Tanzania's Central Bank and Monetary Policy

Introduction to Central Banking

The Bank of Tanzania (BoT) serves as the nation's central bank, playing a crucial role in maintaining economic stability and managing the country's monetary policy. Educational tours of the BoT provide students with a unique opportunity to understand how central banking functions and its impact on everyday economic life in Tanzania.

Through guided tours of the central bank facilities, students can learn about currency management, monetary policy implementation, and the bank's role in regulating the financial sector. This experience brings economic theory to life and demonstrates how central banking decisions affect inflation, interest rates, and overall economic growth.

Educational Focus: The tours specifically emphasize the BoT's role in monetary policy, currency management, inflation control, and financial sector regulation, providing students with practical understanding of macroeconomic management.

Educational Benefits for Students

Visiting the Bank of Tanzania offers students numerous educational benefits that complement their classroom learning in economics, commerce, and social studies:

💰

Understanding National Currency

Students learn about the Tanzanian Shilling - its design, security features, and the process of currency issuance and management.

📈

Inflation Management

Students comprehend how the central bank uses monetary policy tools to control inflation and maintain price stability.

🏦

Financial Sector Role

Understanding the BoT's crucial role as banker to the government and regulator of commercial banks and financial institutions.

🌍

Economic Stability

Learning how central bank policies contribute to national economic stability and sustainable growth.

💡

Monetary Policy Tools

Understanding the instruments used by the central bank to influence money supply and interest rates.

💼

Career Inspiration

Exposure to central banking operations can inspire interest in economics, finance, and banking careers.

National Currency: The Tanzanian Shilling

The Bank of Tanzania is responsible for issuing and managing the Tanzanian Shilling (TZS), the national currency. During educational tours, students learn about various aspects of currency management:

500 TZS

Features Julius Nyerere

1,000 TZS

Lion design

2,000 TZS

Black rhinoceros

5,000 TZS

Elephant design

10,000 TZS

Bank of Tanzania building

Currency Security Features:

• Watermarks: Hidden images visible when held to light
• Security Threads: Metallic strips embedded in the paper
• Color-Shifting Ink: Ink that changes color when tilted
• Microprinting: Tiny text that is difficult to reproduce
• Holographic Strips: Reflective strips with 3D effects

Understanding and Managing Inflation

One of the Bank of Tanzania's primary responsibilities is controlling inflation to maintain price stability and preserve the value of the Tanzanian Shilling.

Causes of Inflation in Tanzania:

Demand-Pull Inflation

When aggregate demand exceeds the economy's productive capacity, leading to price increases.

Cost-Push Inflation

Rising production costs (imported goods, wages, raw materials) that force businesses to increase prices.

Monetary Inflation

Excessive growth in money supply without corresponding increase in goods and services.

Imported Inflation

Price increases due to rising costs of imported goods and currency depreciation.

How BoT Manages Inflation:

• Interest Rate Policy: Adjusting policy rates to influence borrowing costs
• Reserve Requirements: Setting minimum reserves commercial banks must hold
• Open Market Operations: Buying and selling government securities to influence money supply
• Foreign Exchange Intervention: Managing exchange rate stability
• Inflation Targeting: Setting and communicating clear inflation targets

Currency Production and Security

The Bank of Tanzania oversees the production and distribution of the national currency, ensuring adequate supply while maintaining security and integrity.

Where Money is Printed:

The Bank of Tanzania works with specialized security printing companies, both domestic and international, to produce banknotes. These facilities implement extreme security measures to prevent counterfeiting and ensure the integrity of the currency.

Currency Production Process:

1. Design Phase: Creating currency designs with advanced security features
2. Printing: Using specialized printing techniques on security paper
3. Quality Control: Rigorous inspection of each banknote
4. Distribution: Secure transportation to Bank of Tanzania branches
5. Circulation: Distribution to commercial banks and ultimately to the public

Educational Insight: Students learn that currency production involves sophisticated technology and multiple security layers to prevent counterfeiting and maintain public confidence in the monetary system.

BoT Collaboration with Commercial Banks

The Bank of Tanzania maintains a crucial relationship with commercial banks, serving as both regulator and partner in the financial system.

Regulatory Functions

• Licensing and Supervision: Granting banking licenses and monitoring compliance
• Prudential Regulations: Setting capital adequacy and risk management standards
• Monetary Policy Implementation: Using commercial banks to transmit policy changes
• Payment System Oversight: Ensuring smooth operation of national payment systems

Operational Cooperation

• Lender of Last Resort: Providing emergency liquidity to solvent banks
• Currency Distribution: Supplying cash to meet public demand
• Clearing and Settlement: Operating interbank payment systems
• Financial Stability: Collaborating to maintain overall financial system stability

Monetary Policy Transmission:

🏦

Policy Rate

Central bank interest rate that influences commercial bank rates

📊

Reserve Ratio

Percentage of deposits banks must hold as reserves

💵

Open Market Operations

Buying/selling government securities to adjust money supply

🌐

Foreign Exchange

Intervening in forex markets to stabilize currency

Tour Information and Educational Activities

Student tours of the Bank of Tanzania are carefully structured to provide maximum educational value while maintaining security and operational requirements:

Typical Tour Structure:

• Orientation Session: Introduction to central banking functions and monetary policy
• Currency Exhibition: Viewing currency displays and learning about security features
• Educational Workshop: Interactive session on economic concepts and banking operations
• Museum Visit: Exploring the history of money and banking in Tanzania
• Q&A Session: Opportunity to ask questions to BoT officials and economists

Tour Educational Highlights:

💰

Learning about currency design and security features

📈

Understanding inflation measurement and control mechanisms

🏦

Discovering the role of central banks in economic stability

🔍

Exploring how monetary policy affects everyday life

💡

Learning about career opportunities in central banking

🌍

Understanding Tanzania's position in the global economy

Conclusion: The Importance of Central Bank Education

Educational tours of the Bank of Tanzania provide students with invaluable insights into the functioning of a modern central bank and its critical role in maintaining economic stability. These experiences transform abstract economic concepts into tangible realities, helping students understand how monetary policy decisions affect their daily lives, from the prices they pay for goods to the stability of their savings.

By learning about currency management, inflation control, and financial sector regulation, students develop a deeper appreciation for the importance of sound economic management. This knowledge empowers them to become more informed citizens who can better understand economic news and policy debates.

Long-term Impact: Beyond immediate educational benefits, central bank tours can inspire future economists, bankers, and policymakers, create greater public understanding of monetary policy, and contribute to economic literacy in the next generation of Tanzanian leaders.

Disclaimer: This educational resource provides general information about student tours of the Bank of Tanzania. Specific tour arrangements must be coordinated with bank authorities and are subject to security protocols and operational requirements.

© 2026 Educational Resources - Bank of Tanzania Tours

10 Strategies to Get an A in Form Four History

Master historical analysis, chronology, and critical thinking for exam success

History is more than just memorizing dates and events—it's about understanding patterns, analyzing causes and effects, and developing critical thinking skills. Excelling in Form Four History requires mastering both content knowledge and historical methodology. These 10 proven strategies will help you analyze historical events, construct compelling arguments, and achieve that coveted A grade in your examinations.

1 Master Chronological Understanding

Create detailed timelines for each historical period. Understand not just when events happened, but how they connect to each other in sequence and causation.

Example:

For African independence movements:
1957: Ghana gains independence (first sub-Saharan African colony)
1960: "Year of Africa" - 17 nations gain independence
1961: Tanganyika gains independence
1963: OAU formed to promote African unity
1964: Zanzibar Revolution and union with Tanganyika

2 Analyze Causes and Consequences

For every major event, identify and categorize causes (political, economic, social) and consequences (short-term and long-term impacts).

Example:

First World War Causes:
• Political: Alliance systems, imperialism
• Economic: Industrial competition, arms race
• Social: Nationalism, militarism

Consequences for Africa:
• Economic exploitation intensified
• Rise of African nationalism
• League of Nations mandate system

3 Master Key Historical Concepts

Understand and apply historical concepts like change and continuity, significance, causation, and historical interpretation in your answers.

Example:

Change and Continuity: In colonial Africa, political systems changed (from traditional to colonial administration) while some cultural practices continued.

Historical Significance: Explain why the Maji Maji Rebellion (1905-1907) was significant: it demonstrated African resistance to German rule, united different ethnic groups, and influenced later nationalist movements.

4 Develop Source Analysis Skills

Learn to evaluate primary and secondary sources for reliability, bias, purpose, and historical context. Practice comparing different perspectives.

Example:

When analyzing a colonial administrator's report about African resistance:
• Consider the author's perspective (colonial official)
• Identify potential bias (justifying colonial rule)
• Evaluate purpose (report to superiors, possibly to request more troops)
• Compare with African oral traditions about the same events

5 Master Essay Structure for Historical Arguments

Develop clear, well-structured essays with strong thesis statements, supported by specific historical evidence and analysis.

Example:

Essay Structure:
Introduction: Context + clear thesis statement ("The Scramble for Africa was primarily driven by economic factors rather than political rivalries")
Body Paragraphs: Each with topic sentence, evidence (specific examples), explanation, and link back to thesis
Conclusion: Restate thesis in light of evidence, summarize key points, broader historical significance

6 Use Specific Historical Evidence

Support your arguments with precise facts, dates, names, statistics, and specific examples rather than general statements.

Example:

Instead of: "Colonialism had economic impacts"

Write: "The Groundnut Scheme in Tanganyika (1947-1952) failed due to poor planning, costing £36 million and demonstrating how colonial economic projects often overlooked local conditions and knowledge."

7 Create Comparative Analysis Frameworks

Develop skills to compare and contrast historical events, movements, or periods. Identify similarities, differences, and reasons for variations.

Example:

Compare independence movements in Ghana and Tanzania:
Similarities: Both used political parties (CPP vs TANU), both leaders educated abroad (Nkrumah vs Nyerere), both achieved independence through negotiation
Differences: Ghana had mass protests and strikes, Tanganyika had more gradual transition; Nkrumah emphasized Pan-Africanism immediately, Nyerere focused on national unity first

8 Master Historical Terminology

Use precise historical vocabulary to demonstrate understanding of concepts and periods. Avoid anachronisms and modern judgments.

Example:

Correct usage of terms:
• Imperialism vs Colonialism
• Nationalism vs Patriotism
• Primary source vs Secondary source
• Historical context - understanding events within their time period

9 Practice with Past Papers and Marking Schemes

Regularly attempt past examination questions under timed conditions. Study marking schemes to understand what examiners look for.

Example:

When practicing essay questions:
• Allocate time: 5-10 minutes planning, 25-30 minutes writing, 5 minutes checking
• Note command words: "Analyze" requires breaking down, "Evaluate" requires judgment
• Check marking scheme: Usually awards marks for knowledge, understanding, analysis, and structure
• Practice writing to the point - avoid irrelevant information

10 Create Visual Learning Aids

Use mind maps, flowcharts, and diagrams to organize complex historical information and show relationships between events and concepts.

Example:

Mind Map for Causes of WWII:
Central topic: WWII Causes
Main branches: Treaty of Versailles, Failure of League of Nations, Rise of Dictators, Economic Factors, Appeasement Policy
Sub-branches: Under Treaty of Versailles - German resentment, territorial losses, reparations

Flowchart for Decolonization: Colonial Rule → African Resistance → World War II Impact → Rise of Nationalism → Independence Movements → Independence

For More Resources and Past Papers

Contact MITIHANI POPOTE for comprehensive exam preparation materials

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MITIHANI POPOTE PHYSICS 2 SERIES 1 (With detailed Solutions)

MITIHANI POPOTE
MITIHANI POPOTE EXAMIANTION SERIES

PHYSICS 2 - SERIES 1

131/02
TIME: 2:30 HRS
2025

INSTRUCTIONS

1. This paper consists of six (06) questions.
2. Answer five (5) questions.
3. Each question carries twenty (20) marks.
4. Mathematical tables and non-programmable calculators may be used.
5. Cellular phones and any unauthorized materials are not allowed in the examination room.
6. Write your examination number on every page of your answer sheet/booklet(s).

The following information may be useful:

• Acceleration due to gravity \( g = 9.8 \text{m/s}^2 \)
• Density of water, \( pw = 10^3 \text{kg} \text{m}^{-3} \)
• Density of air, \( \rho_{\text{air}} = 1.29 \text{kg/m}^3 \)
• Density of mercury \( = 13.6 \times 10^3 \text{kg/m}^3 \)
• Coefficient of viscosity of water \( = 1.0 \times 10^{-3} \text{Ns} \text{m}^{-2} \)
• Velocity of sound in air, \( V = 330 \text{m/s} \)
• Coefficient of linear expansion of copper \( = 8 \times 10^{-6} \text{°C} \)
• Bulk modulus of elasticity of cooper \( = 3.6 \times 10^{11} \text{N/m}^2 \)
• Surface tension of water \( = 7.2 \times 10^{-2} \text{N/m} \)
• Permeability of free space, \( \mu_0 = 4 \pi \times 10^{-7} \text{Hm}^{-1} \)
• Permittivity of free space, \( \epsilon_0 = 8.854 \times 10^{-12} \text{Fm}^{-1} \)
• Mass of \( \frac{3}{2} \text{Ca} = 39.962589u \)
• Mass of neutron, \( \text{Mn} = 1.008665u \)
• Mass of proton, \( \text{Mp} = 1.007825u \)
• Universal gas constant, \( R = 8.31 \text{J/molK} \)
• Young modulus of aluminium, \( \text{Yal} = 7 \times 10^{10} \text{Nm}^{-2} \)
• Boltzman constant \( (K_p) = 1.38 \times 10^{-23} \text{J/K} \)
• Electronic charge, \( e = 1.6 \times 10^{-19} \text{C} \)
• Avogadro’s number, \( NA = 6.0 \times 10^{23} \text{mole} \)
• Mass of electron, \( Me = 9.1 \times 10^{-31} \text{kg} \)
• Planck’s constant, \( h = 6.62 \times 10^{-34} \text{s} \)
• Pie, \( \pi = 3.14 \)

Page 1 of 4

Answer five questions.

1.

(a)

(i) Why rain drop falling under gravity do not acquire very high velocity? (02 marks)

(ii) A sphere is dropped under gravity through a fluid of viscosity, \(\eta\). Taking average acceleration as half of the initial acceleration show that the time taken to attain terminal velocity is independent of fluid density (05 marks)

(b)

(i) Deep water runs slowly. Why? (02 marks)

(ii) If the velocity head of stream of water is equal to 10cm, what is the speed of flow? (02 marks)

(c)

(i) Water flows steadily along the horizontal pipe at a rate of \(8 \times 10^3 m^3/s\). If the area of cross-section of the pipe is \(40 \times 10^{-4} m^2\). Calculate the flow velocity of water. (01 marks)

(ii) Find the total pressure in the pipe if the static pressure in the horizontal pipe is \(3 \times 10^4 Pa\). What is the new velocity if the total pressure is \(3.6 \times 10^4 Pa\)? (03 marks)

(d) Water flows steadily through a tube which consists of two parts joined together end to end, one part is 21cm long and the other is 7cm long and has a diameter of 0.07cm. If the pressure difference between the ends of the tube is 14cm of water. Find the pressure difference between end of each part if the other part has a diameter of 0.225cm (05 marks)

2.

(a)

(i) State Doppler principle concerning with sound waves. (01 marks)

(ii) We cannot hear echo in a room. Explain. (02 marks)

(iii) A man riding a merry - go - round emits a sound of a certain frequency. If another man is at the centre of merry - go - round, will he observe Doppler effect? Explain. (02 marks)

(b)

(i) Identify two distinct examples between transverse waves and longitudinal waves. (02 marks)

(ii) The third overtone of a closed pipe is found to be unison with the first overtone of an open pipe. Find the ratio of the length of the pipe. (03 marks)

(c)

(i) State four conditions for sustainable interference. (02 marks)

(ii) Monochromatic light of wavelength 600nm is incident normally on an optical transmission of spacing 200\(\mu m\). Calculate the number of diffracted beams which can be observed and the maximum order possible. (03 marks)

(d)

(i) Briefly explain, what happen to fringe separation if the slit separation is doubled? (02 marks).

(ii) What is the Brewster angle for air to glass transmission? (03 marks)

Page 2 of 4

3.

(a)

(i) Why does not water comes out of a Doppler unless the rubber bulb is pressed?

(ii) There is a soap bubble of radius \(2.4 \times 10^{-4} m\) in an air cylinder which is originally at a pressure of \(10^5 N/m^2\). The air in the cylinder is now compressed isothermally until the radius of the bubble is halved. Calculate now the pressure of air in the cylinder. The surface tension of soap film is 0.08Nm\(^{-1}\) (04 marks)

(b)

(i) How will the rise of liquid be affected if the top capillary tube is closed? (01 marks)

(ii) Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by \(75 \times 10^{-4} N\) force due to the weight of the liquid. What is the inner radius of the capillary tube? (03 marks)

(c)

(i) What happen to work done during stretching of wire?

(ii) A stone of 0.5kg mass is attached to one end of a 0.8m long aluminium wire of 0.7mm diameter and suspended vertically. The stone is now rotated in a horizontal plane at a rate such that the wire makes an angle of 85° with the vertical. Find the increase in length of the wire. (03 marks)

(d)

(i) In terms of kinetic theory of gases, explain why the pressure of a gas in a container increases when a gas is heated? (03 marks)

(ii) Find the mean free path and collision frequency for nitrogen molecules at a temperature of 20°C and a pressure of 1 a.t.m. Assume a molecular diameter of \(2 \times 10^{-10} m\). Given that the average speed of nitrogen molecule at 20°C is 511m/s.

4.

(a)

(i) What is equipotential surface? (02 marks)

(ii) Give four properties of an equipotential surface. (04 marks)

(b)

(i) State Coulomb’s law of electrostatics. (02 marks)

(ii) Two electric charges q and 4q are placed at a distance of 6cm apart on a horizontal plane. Find the locus of the point on the line joining the two charges where the electric field is zero. (03 marks)

(c) Give reason(s) for the following statements:

i. When we introduce a dielectric slab between plates of a charged air capacitor, its capacitance increases (03 marks)

ii. Any conducting object connected to earth is said to be grounded (03 marks)

(d) A 500μF capacitor with a charge of 300μC is discharged through 200kΩ resistor. What is the current after 20s? (03 marks)

Page 3 of 4

5.

(a)

(i) State the Biot – savart law and use it to derive the expression of magnetic field at the centre of current carrying circular coil (04 marks)

(ii) The electron of hydrogen atom moves along a circular pass of radius 0.5nm with a uniform speed of \(4.0 \times 10^6 m/s\). Calculate the magnetic field produced by the electron at the centre. (02 marks)

(b)

(i) How does “one ampere” is defined in the concept of magnetic force? (02 marks)

(ii) State the rule which gives the direction of force experienced by a straight current carrying conductor placed in a magnetic field (02 marks)

(c) Calculate the force per unit length on a long straight wire carrying a current of 6A in opposite direction. Distance between the wires is 3cm. State the direction of the force. (04 marks)

(d)

(i) State Faraday’s law of electromagnetic induction. (02 marks)

(ii) Which factors determine the magnitude of e.m.f induced in a coil? \(\left(1 \frac{1}{2}\right)\)

6.

(a)

(i) Define activity of radioactive decay (01 marks)

(ii) Derive an expression for the activity constant in terms of half-life. (03 marks)

(iii) A radioactive isotope Cobalt 60 is widely used in medicine and has a half-life of about 5.3 years. What mass of the isotope is required for the activity of 1 millicurie? (04 marks)

(b)

(i) What is the meaning of negative energy of orbiting electron? (01 marks)

(ii) Differentiate between Rutherford’s model and Bohr’s model of an atom. Give two differences. (03 marks)

(iii) Calculate the time taken by an electron to travel the first Bohr orbit in the hydrogen atom. (03 marks)

(c)

(i) How do you account for the stability of a nucleus? (02 mark)

(ii) It is proposed that to use the nuclear fusion reaction; \(1^{H^2} + 1^{H^2} \rightarrow 2^{He^4}\) in a nuclear reactor of 200MW rating. If the energy from the above reaction is used with 25% efficiency in the reactor, how many grams of deuterium fuel will be needed per day? The masses of \(1^{H^2}\) and \(2^{He^4}\) are 2.0141a.m.u and 4.0026a.m.u respectively. (04 marks)

Page 4 of 4

End of Examination Paper

MITIHANI POPOTE

EXAMIANTION SERIES

SERIES PHYSICS 2 - SERIES 1

Code: 131/02

TIME: 2:30 HRS

JANUARY-MAY, 2023

INSTRUCTIONS

1. This paper consists of six (06) questions.
2. Answer five (5) questions.
3. Each question carries twenty (20) marks.
4. Mathematical tables and non-programmable calculators may be used.
5. Cellular phones and any unauthorized materials are not allowed in the examination room.
6. Write your examination number on every page of your answer sheet/booklet(s).

The following information may be useful:

Acceleration due to gravity \( g = 9.8 \text{m/s}^2 \)

Density of water, \( \rho_w = 10^3 \text{kg} \text{m}^{-3} \)

Density of air, \( \rho_{\text{air}} = 1.29 \text{kg/m}^3 \)

Density of mercury \( = 13.6 \times 10^3 \text{kg/m}^3 \)

Coefficient of viscosity of water \( = 1.0 \times 10^{-3} \text{Ns} \text{m}^{-2} \)

Velocity of sound in air, \( V = 330 \text{m/s} \)

Electronic charge, \( e = 1.6 \times 10^{-19} \text{C} \)

Mass of electron, \( m_e = 9.1 \times 10^{-31} \text{kg} \)

Planck's constant, \( h = 6.62 \times 10^{-34} \text{Js} \)

Answer five questions.

Question 1

20 marks

(a) (i) Why rain drop falling under gravity do not acquire very high velocity? (02 marks)

Answer:

Raindrops do not acquire very high velocity due to air resistance. As a raindrop falls, the force of gravity accelerates it downward. However, as its velocity increases, the air resistance (drag force) opposing its motion also increases. Eventually, the drag force equals the gravitational force, and the raindrop reaches a constant velocity known as terminal velocity.

(a) (ii) A sphere is dropped under gravity through a fluid of viscosity, \(\eta\). Taking average acceleration as half of the initial acceleration show that the time taken to attain terminal velocity is independent of fluid density (05 marks)

Answer:

Let's denote:

• m = mass of sphere
• r = radius of sphere
• ρ = density of sphere
• σ = density of fluid
• η = viscosity of fluid
• v_t = terminal velocity

The forces acting on the sphere are:

Weight downward: \( W = mg = \frac{4}{3}\pi r^3 \rho g \)

Buoyant force upward: \( F_b = \frac{4}{3}\pi r^3 \sigma g \)

Viscous drag upward: \( F_d = 6\pi \eta r v \) (Stokes' law)

Net force: \( F_{net} = W - F_b - F_d = \frac{4}{3}\pi r^3 (\rho - \sigma)g - 6\pi \eta r v \)

At terminal velocity, F_net = 0:

\( \frac{4}{3}\pi r^3 (\rho - \sigma)g = 6\pi \eta r v_t \)

\( v_t = \frac{2}{9} \frac{r^2 (\rho - \sigma)g}{\eta} \)

Initial acceleration (when v=0):

\( a_i = \frac{W - F_b}{m} = \frac{\frac{4}{3}\pi r^3 (\rho - \sigma)g}{\frac{4}{3}\pi r^3 \rho} = \frac{(\rho - \sigma)g}{\rho} \)

Average acceleration: \( a_{avg} = \frac{1}{2}a_i = \frac{(\rho - \sigma)g}{2\rho} \)

Time to reach terminal velocity: \( t = \frac{v_t}{a_{avg}} = \frac{\frac{2}{9} \frac{r^2 (\rho - \sigma)g}{\eta}}{\frac{(\rho - \sigma)g}{2\rho}} = \frac{4}{9} \frac{r^2 \rho}{\eta} \)

This expression for time is independent of fluid density (σ), proving the required result.

(b) (i) Deep water runs slowly. Why? (02 marks)

Answer:

According to the equation of continuity for incompressible fluids (A₁v₁ = A₂v₂), when water flows from a shallow region to a deep region, the cross-sectional area increases. To maintain the same flow rate, the velocity must decrease. Therefore, deep water runs slowly compared to shallow water.

(b) (ii) If the velocity head of stream of water is equal to 10cm, what is the speed of flow? (02 marks)

Answer:

Velocity head is given by \( h = \frac{v^2}{2g} \)

Given h = 10 cm = 0.1 m, g = 9.8 m/s²

\( v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 0.1} = \sqrt{1.96} = 1.4 \, \text{m/s} \)

The speed of flow is 1.4 m/s.

Question 2

20 marks

(a) (i) State Doppler principle concerning with sound waves. (01 marks)

Answer:

The Doppler principle states that the apparent frequency of a sound wave changes when there is relative motion between the source of sound and the observer. The frequency increases when the source and observer are moving toward each other and decreases when they are moving apart.

(a) (ii) We cannot hear echo in a room. Explain. (02 marks)

Answer:

We cannot hear echo in a typical room because:

1. The distance between the sound source and reflecting surfaces is too small. For a distinct echo to be heard, the reflecting surface should be at least 17 meters away (so that the time delay is at least 0.1 seconds).
2. In rooms, multiple reflections (reverberations) occur from various surfaces, causing the sound to persist rather than producing a distinct echo.
3. Sound-absorbing materials in rooms (like furniture, carpets, curtains) reduce reflection intensity.

Question 3

20 marks

(a) (i) Why does not water comes out of a dropper unless the rubber bulb is pressed?

Answer:

Water does not come out of a dropper unless the rubber bulb is pressed due to:

1. Atmospheric pressure: The atmospheric pressure acting on the surface of the liquid in the dropper is greater than the pressure inside the dropper when the bulb is released.
2. Surface tension: The surface tension of water creates a "skin" that prevents water from flowing out freely.
3. Adhesive forces: Water molecules adhere to the glass surface of the dropper, creating a meniscus that resists flow.

When the bulb is pressed, the air pressure inside increases, overcoming these forces and pushing the liquid out.

Question 4

20 marks

(a) (i) What is equipotential surface? (02 marks)

Answer:

An equipotential surface is a surface in a field (electric or gravitational) where every point on the surface has the same potential. In an electric field, it's a surface where the electric potential is constant. No work is done when moving a charge along an equipotential surface.

Question 5

20 marks

(a) (i) State the Biot-Savart law and use it to derive the expression of magnetic field at the centre of current carrying circular coil (04 marks)

Answer:

Biot-Savart Law: The magnetic field dB due to a current element Idl at a point P is given by:

\( d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2} \)

where:

• μ₀ is the permeability of free space
• I is the current
• dl is the length element of the conductor
• r is the distance from the element to point P
• ŕ is the unit vector in the direction from dl to P

Derivation for magnetic field at center of circular coil:

Consider a circular coil of radius R carrying current I. For an element dl at the circumference:

• The angle between dl and r is 90°
• The distance from dl to center is R
• All dB contributions are in the same direction (perpendicular to the plane of the coil)

\( dB = \frac{\mu_0}{4\pi} \frac{I dl \sin 90^\circ}{R^2} = \frac{\mu_0}{4\pi} \frac{I dl}{R^2} \)

Integrating over the entire circumference (∫dl = 2πR):

\( B = \int dB = \frac{\mu_0}{4\pi} \frac{I}{R^2} \int dl = \frac{\mu_0}{4\pi} \frac{I}{R^2} (2\pi R) \)

\( B = \frac{\mu_0 I}{2R} \)

This is the magnetic field at the center of a circular current-carrying coil.

Question 6

20 marks

(a) (i) Define activity of radioactive decay (01 marks)

Answer:

Activity of radioactive decay is defined as the rate at which radioactive nuclei decay. It is measured in becquerels (Bq) where 1 Bq = 1 decay per second. The activity A is given by A = λN, where λ is the decay constant and N is the number of radioactive nuclei.

End of Examination Paper with Detailed Answers