All practice questions

Question 13701Question →

The derived SI unit of electric capacitance, the farad ( $\text{F}$ ), can be expressed in terms of fundamental SI base units as $\text{kg}^a \cdot \text{m}^b \cdot \text{s}^c \cdot \text{A}^d$ . What is the numerical value of the sum of the exponents $a + b + c + d$ ?

Show answer & explanation

Answer: 3

Answer

The numerical value of the sum of the exponents

a + b + c + d

is 3.

The farad (

\text{F}

), when resolved into fundamental SI base units, is

\text{kg}^{-1} \cdot \text{m}^{-2} \cdot \text{s}^4 \cdot \text{A}^2

. Adding the exponents yields

a = -1

,

b = -2

,

c = 4

, and

d = 2

, giving a total sum of

(-1) + (-2) + 4 + 2 = 3

.

Step-by-Step Solution

1

Relate electric capacitance to fundamental physical quantities

Capacitance is defined as

C = \frac{Q}{V}

, where

Q

is electric charge and

V

is electric potential difference.

This fundamental relation connects capacitance to charge and energy per unit charge.

2

Express charge and potential difference in terms of SI base units

Electric charge

Q

has base units

\text{A} \cdot \text{s}

. Potential difference

V = \frac{\text{Work}}{Q}

has base units

\frac{\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2}}{\text{A} \cdot \text{s}} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-3} \cdot \text{A}^{-1}

.

Work is force times distance (

\text{kg} \cdot \text{m} \cdot \text{s}^{-2} \times \text{m} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2}

) and electric current is a fundamental base quantity.

3

Determine the base unit representation of the farad

The farad is expressed as

\frac{\text{A} \cdot \text{s}}{\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-3} \cdot \text{A}^{-1}} = \text{kg}^{-1} \cdot \text{m}^{-2} \cdot \text{s}^4 \cdot \text{A}^2

.

Dividing the unit of charge by the unit of potential difference yields the derived base unit expression.

4

Calculate the sum of the exponents

a + b + c + d = (-1) + (-2) + 4 + 2 = 3

.

Summing the powers corresponding to kilograms, meters, seconds, and amperes gives the final scalar value.

Key Concept

Expressing derived SI units in terms of fundamental SI base units

Question 13702Question →

A haulage enterprise in Nigeria seeking a commercial bank loan to expand its truck fleet was required to provide comprehensive insurance cover for the vehicles before the funds were disbursed. Which of the following best explains how insurance facilitates credit creation in this commercial scenario?

It enhances creditworthiness by safeguarding pledged collateral against loss or damage.

It eliminates the physical occurrence of accidents and operational hazards during transport.

It guarantees pre-determined operational profits for the haulage business regardless of market conditions.

It transfers the primary obligation of repaying the bank loan from the firm to the insurer.

Show answer & explanation

Answer: It enhances creditworthiness by safeguarding pledged collateral against loss or damage.

Answer

It enhances creditworthiness by safeguarding pledged collateral against loss or damage.

Insurance serves as an essential aid to business by facilitating credit procurement. By insuring assets pledged as security, the business guarantees that the lender will not lose financial backing if the asset is damaged, thereby boosting creditworthiness.

Step-by-Step Solution

1

Identify the key role of insurance illustrated in the scenario.

The scenario focuses on insurance as an aid to securing business credit and loan facilities.

When commercial firms borrow funds using tangible assets as collateral, financial institutions demand protection against asset destruction.

2

Analyze how insurance protects the financial institution's interest.

If the asset is damaged or lost, insurance indemnifies the loss, ensuring the security backing the loan remains intact.

This risk reduction encourages banks and creditors to extend financial credit to businesses.

Key Concept

Role of Insurance in Credit Procurement and Security of Collateral

Question 13703Question →

An electric lamp rated $60\,\text{W}$ operates normally when connected to a $240\,\text{V}$ mains supply. What is the electric current drawn by the lamp?

0.25\,\text{A}

4.0\,\text{A}

2.5\,\text{A}

14\,400\,\text{A}

Show answer & explanation

Answer: $0.25\,\text{A}$

Answer

The electric current drawn by the lamp is

0.25\,\text{A}

.

Electric power is defined by the formula

P = IV

, where

P

is power in watts,

I

is current in amperes, and

V

is potential difference in volts. Rearranging to solve for current yields

I = \frac{P}{V}

. Substituting

60\,\text{W}

for power and

240\,\text{V}

for voltage gives

I = \frac{60}{240} = 0.25\,\text{A}

.

Step-by-Step Solution

1

Identify given parameters and state the electric power formula.

Power

P = 60\,\text{W}

and voltage

V = 240\,\text{V}

. Power is related to current and voltage by

P = IV

.

Electric power dissipated by a component is the product of current and voltage across it.

2

Rearrange the formula to solve for current

I

.

I = \frac{P}{V}

Making current

I

the subject of the equation.

3

Substitute the values into the formula and solve.

I = \frac{60\,\text{W}}{240\,\text{V}} = 0.25\,\text{A}

Dividing

60

by

240

gives

0.25

amperes.

Key Concept

Relationship between Electrical Power, Voltage, and Current

Question 13704Question →

Despite lacking local iron ore deposits and primary steel smelting infrastructure, Nnewi in Anambra State has developed into a major industrial center in Nigeria specializing in vehicle spare parts production and light engineering. Which of the following factors primarily accounts for the growth and localization of this industrial cluster?

Proximity to heavy weight-losing raw materials utilized in automotive casting

Accumulation of commercial capital, skilled entrepreneurial labor, and strong market demand

Direct access to rich iron ore reserves extracted within the immediate river basin

State-mandated relocation of government heavy metallurgical plants to rural agricultural zones

Show answer & explanation

Answer: Accumulation of commercial capital, skilled entrepreneurial labor, and strong market demand

Answer

The growth and localization of the Nnewi industrial cluster is primarily driven by the accumulation of commercial capital, skilled entrepreneurial labor, and strong market demand.

The industrial cluster at Nnewi developed through private entrepreneurship, reinvestment of trading capital, skilled artisan craftsmanship, and high market demand for auto components across West Africa. Because light engineering is relatively footloose, proximity to primary raw material deposits was not a prerequisite for its success.

Step-by-Step Solution

1

Identify the key characteristics of the manufacturing sector in Nnewi, Anambra State.

Nnewi is known for vehicle spare parts, plastics, and light engineering industries.

Understanding the output of the industrial center helps determine its location requirements.

2

Evaluate Weber's industrial location factors in the context of footloose and light assembly manufacturing.

Light engineering items are high in value relative to weight and rely heavily on capital, technical skills, and market access rather than bulk raw materials.

Footloose industries locate where market linkages and human resources are optimized.

3

Select the primary factor explaining Nnewi's unique industrial development.

Private capital built through trading networks combined with local artisan skills fostered industrial agglomeration in Nnewi.

Commercial capital and entrepreneurship are the decisive growth drivers for this cluster.

Key Concept

Industrial Location Factors and Agglomeration in Nigeria

Estimated Time:1m 15s

Question 13705Question →

A cocoa farmer in Ondo State harvests raw cocoa beans and sells them to a processing factory in Ikeja that transforms them into chocolate bars. A logistics firm transports the finished products to wholesalers nationwide, while an insurance company covers the risk of loss during transit. Which of the following best explains the inter-relationship between industry, commerce, and occupation illustrated in this scenario?

Industry creates form utility by transforming raw materials into finished goods, commerce provides place and time utility through distribution and auxiliaries, while commercial occupations facilitate the entire chain.

Industry is strictly confined to cocoa farming, commerce consists solely of buying and selling chocolate, and insurance personnel perform direct service occupations.

Both cocoa farming and chocolate processing belong to the extractive sector of industry, while transport workers engage in primary occupations.

The transport and insurance services represent direct production for self-consumption, which operates independently of commercial occupations.

Show answer & explanation

Answer: Industry creates form utility by transforming raw materials into finished goods, commerce provides place and time utility through distribution and auxiliaries, while commercial occupations facilitate the entire chain.

Answer

Industry creates form utility by transforming raw materials into finished goods, commerce provides place and time utility through distribution and auxiliaries, while commercial occupations facilitate the entire chain.

The correct response accurately reflects the systemic inter-relationship: industry (farming and factory processing) provides goods by creating form utility, commerce (transportation and insurance) bridges the spatial and temporal gap between producer and consumer, and commercial occupations carry out these essential activities.

Step-by-Step Solution

1

Identify the industrial stage

Cocoa farming represents primary (extractive) industry, while processing cocoa beans into chocolate represents secondary (manufacturing) industry.

Industry involves extracting raw materials and converting them into useful finished products.

2

Analyze the commercial link and auxiliaries

Transportation moves the goods (place utility) and insurance protects against risks, forming essential auxiliaries to trade.

Commerce encompasses trade and all services that assist in moving goods from producers to consumers.

3

Connect to occupational roles

Workers in transport, insurance, and trade operate within commercial occupations that bind industry to consumer satisfaction.

Occupations are classified based on the nature of employment provided across the chain of production and distribution.

Key Concept

Inter-dependence of Industry, Commerce, and Occupation in Production

Question 13706Question →

A glass vessel has a linear expansivity of $9.0 \times 10^{-6}\text{ K}^{-1}$ . When filled to the brim with $500\text{ cm}^3$ of a liquid at $20^\circ\text{C}$ and heated to $70^\circ\text{C}$ , $12\text{ cm}^3$ of the liquid overflows. What is the real cubic expansivity of the liquid?

4.80 \times 10^{-4}\text{ K}^{-1}

4.89 \times 10^{-4}\text{ K}^{-1}

5.07 \times 10^{-4}\text{ K}^{-1}

4.53 \times 10^{-4}\text{ K}^{-1}

Show answer & explanation

Answer: $5.07 \times 10^{-4}\text{ K}^{-1}$

Answer

The real cubic expansivity of the liquid is

5.07 \times 10^{-4}\text{ K}^{-1}

.

The real cubic expansivity of a liquid accounts for both the liquid's apparent expansion (overflow volume) and the expansion of the containing vessel. Calculating the apparent expansivity gives

\gamma_a = 12 / (500 \times 50) = 4.80 \times 10^{-4}\text{ K}^{-1}

. Combining this with the vessel's cubical expansivity

\gamma_v = 3 \times 9.0 \times 10^{-6} = 2.70 \times 10^{-5}\text{ K}^{-1}

yields

\gamma_r = 4.80 \times 10^{-4} + 0.27 \times 10^{-4} = 5.07 \times 10^{-4}\text{ K}^{-1}

.

Step-by-Step Solution

1

Calculate the temperature change (

\Delta T

) and the apparent cubic expansivity (

\gamma_a

).

\Delta T = 70^\circ\text{C} - 20^\circ\text{C} = 50\text{ K}

.

\gamma_a = \frac{\Delta V_a}{V_0 \Delta T} = \frac{12\text{ cm}^3}{500\text{ cm}^3 \times 50\text{ K}} = 4.80 \times 10^{-4}\text{ K}^{-1}

.

Apparent expansion corresponds directly to the volume of liquid that overflows.

2

Calculate the cubic expansivity of the glass vessel (

\gamma_v

).

\gamma_v = 3 \times \alpha_v = 3 \times (9.0 \times 10^{-6}\text{ K}^{-1}) = 2.70 \times 10^{-5}\text{ K}^{-1} = 0.27 \times 10^{-4}\text{ K}^{-1}

.

Cubic expansivity of an isotropic solid container is three times its linear expansivity.

3

Calculate the real cubic expansivity of the liquid (

\gamma_r

).

\gamma_r = \gamma_a + \gamma_v = 4.80 \times 10^{-4}\text{ K}^{-1} + 0.27 \times 10^{-4}\text{ K}^{-1} = 5.07 \times 10^{-4}\text{ K}^{-1}

.

Real cubic expansivity accounts for both the apparent expansion of the liquid and the volume expansion of the container.

Key Concept

Relationship between real cubic expansivity, apparent cubic expansivity, and container volume expansion:

\gamma_r = \gamma_a + \gamma_v

.

Question 13707Question →

In Nigeria, large-scale cattle rearing and nomadic pastoralism are heavily concentrated in the northern savanna region rather than the humid southern forest belt. Which of the following environmental factors is primarily responsible for restricting commercial cattle production in southern Nigeria?

Widespread prevalence of the tsetse fly, which transmits animal trypanosomiasis in humid woodland habitats

Complete absence of perennial river systems and natural water supplies across the southern region

Extremely low atmospheric humidity levels that cause severe thermal stress in livestock

High prevalence of saline soil conditions that prevent the growth of natural pastures and grasses

Show answer & explanation

Answer: Widespread prevalence of the tsetse fly, which transmits animal trypanosomiasis in humid woodland habitats

Answer

Widespread prevalence of the tsetse fly, which transmits animal trypanosomiasis in humid woodland habitats

The humid climate and dense vegetation of the southern forest zone create an ideal habitat for the tsetse fly (*Glossina* spp.), which transmits animal trypanosomiasis (nagana). This disease is fatal to the Zebu cattle breeds raised by Fulani pastoralists, constraining commercial cattle production largely to the tsetse-free northern savannas.

Step-by-Step Solution

1

Analyze spatial distribution of cattle in Nigeria

Cattle production is predominantly concentrated in the open, drier Guinea, Sudan, and Sahel savannas of Northern Nigeria.

Zebu cattle require open grasslands for grazing and dry climate conditions free from heavy humid forest disease vectors.

2

Identify key biological vector limiting southern pastoralism

The tsetse fly (*Glossina* species) thrives in high humidity and dense shade, vectoring trypanosomiasis (nagana).

Trypanosomiasis causes high mortality and morbidity in non-resistant cattle breeds, making permanent cattle keeping in the southern rainforest ecological zone economically unviable.

Key Concept

Environmental controls on pastoralism and cattle distribution in Nigeria

Estimated Time:1m 0s

Question 13708Question →

A rigid gas vessel sealed on a meteorological satellite initially contains a fixed volume of an ideal gas at a pressure of $1.50 \times 10^5\text{ Pa}$ and a temperature of $27^\circ\text{C}$ . During an orbital maneuver, solar radiation heats the vessel to $327^\circ\text{C}$ , while a small vent valve simultaneously allows $20\%$ of the gas molecules to escape. Assuming the volume of the vessel remains constant, what is the final pressure of the gas inside the vessel?

2.40 \times 10^5\text{ Pa}

1.45 \times 10^6\text{ Pa}

3.00 \times 10^5\text{ Pa}

6.00 \times 10^4\text{ Pa}

Show answer & explanation

Answer: $2.40 \times 10^5\text{ Pa}$

Answer

2.40 \times 10^5\text{ Pa}

According to the ideal gas law (

PV = nRT

), when volume is held constant, pressure is directly proportional to both the number of moles of gas present and the absolute temperature in Kelvin (

P \propto nT

). First, convert the initial and final temperatures to Kelvin:

T_1 = 27 + 273 = 300\text{ K}

and

T_2 = 327 + 273 = 600\text{ K}

. Because

20\%

of the gas escapes,

80\%

remains inside the vessel, so

n_2 = 0.80n_1

. Calculating final pressure yields

P_2 = P_1 \times (n_2/n_1) \times (T_2/T_1) = 1.50 \times 10^5 \times 0.80 \times (600/300) = 2.40 \times 10^5\text{ Pa}

.

Step-by-Step Solution

1

Convert all given temperatures from degrees Celsius to absolute temperature in Kelvin.

T_1 = 27 + 273.15 = 300\text{ K}

,

T_2 = 327 + 273.15 = 600\text{ K}

Gas laws and the ideal gas equation require absolute temperature in Kelvin.

2

Determine the fraction of gas remaining in the rigid vessel.

If

20\%

escapes, remaining fraction

n_2 = (1 - 0.20)n_1 = 0.80n_1

Pressure depends on the quantity of gas remaining inside the fixed volume.

3

Apply the ideal gas equation

PV = nRT

for constant volume

V

.

P_2 = P_1 \times \left(\frac{n_2}{n_1}\right) \times \left(\frac{T_2}{T_1}\right)

Since volume is constant, pressure is directly proportional to the product of amount of gas and absolute temperature.

4

Substitute known values to compute the final pressure

P_2

.

P_2 = (1.50 \times 10^5\text{ Pa}) \times 0.80 \times \left(\frac{600\text{ K}}{300\text{ K}}\right) = 2.40 \times 10^5\text{ Pa}

Multiplying the initial pressure by the mole fraction ratio and temperature ratio gives the final gas pressure.

Key Concept

Ideal Gas Equation and Combined Gas Behavior

Estimated Time:2m 0s

Question 13709Question →

A commercial enterprise is modernizing its administrative procedures by integrating specialized office automation technologies to facilitate virtual business operations. Match each office automation tool listed on the left with its primary operational function on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Optical Character Recognition (OCR) System matches with converting physical paper records into editable digital text files. Virtual Data Room (VDR) matches with providing a secure cloud-based repository for sharing confidential documents during corporate due diligence. Remote Desktop Interface matches with enabling remote workers to access central office applications. Transaction Processing System (TPS) matches with recording and processing high-volume daily operational activities.

Each technology corresponds precisely to its administrative and operational application: OCR converts paper documents to digital text, VDR provides a secure environment for confidential due diligence documents, Remote Desktop Interfaces support virtual working by granting access to central office computers, and TPS manages routine operational sales and inventory transactions.

Step-by-Step Solution

1

Analyze the primary role of digitizing paper inputs in office automation.

Optical Character Recognition (OCR) system scans physical paper records and converts image text into editable digital data format.

OCR bridges traditional paper record-keeping with automated electronic workflows.

2

Examine secure document sharing solutions for virtual business transactions.

A Virtual Data Room (VDR) offers strict access controls and encryption for sharing confidential files during legal or corporate restructuring.

VDRs facilitate secure due diligence without physical file distribution.

3

Evaluate telecommuting infrastructure connecting off-site staff to office systems.

Remote Desktop Interface grants virtual access to centralized workstations and proprietary enterprise software.

Remote desktop protocols sustain virtual business operations across geographically dispersed staff.

4

Identify the foundational automation system for daily commercial transactions.

Transaction Processing System (TPS) handles routine high-volume data such as sales receipts, billings, and stock records.

TPS serves as the fundamental operational data collector in modern commercial enterprises.

Key Concept

Office Automation Systems and Virtual Business Technologies

Estimated Time:1m 30s

Question 13710Question →

Which of the following environmental and structural characteristics of African equatorial rainforests presents the primary obstacle to large-scale, cost-effective commercial timber extraction?

The high degree of tree species heterogeneity, where economic timber trees are widely scattered among non-commercial varieties

The dominance of softwoods such as pine and fir, which rot quickly under humid tropical conditions

The complete absence of navigable river networks needed for floating logs to processing centers

The presence of uniform single-species stands that lead to rapid market saturation and price drops

Show answer & explanation

Answer: The high degree of tree species heterogeneity, where economic timber trees are widely scattered among non-commercial varieties

Answer

The high degree of tree species heterogeneity, where economic timber trees are widely scattered among non-commercial varieties

The correct answer highlights tree species heterogeneity. In African tropical rainforests, commercially valuable timber species like Mahogany, Sapele, and Iroko grow widely dispersed among hundreds of non-commercial tree species per hectare. This dispersion requires building extensive transport tracks to cut down isolated trees, making commercial operations capital-intensive and complex.

Step-by-Step Solution

1

Analyze the ecological structure of African equatorial rainforests.

Equatorial rainforests exhibit extremely high biodiversity, with hundreds of distinct tree species intermingled within a small area.

Commercial lumbering relies on specific valuable hardwood species like Iroko, Mahogany, and Ebony.

2

Evaluate how species heterogeneity impacts commercial harvesting efficiency.

Because desirable timber species do not grow in pure, homogeneous stands, lumbermen must construct long haulage roads through dense forest to locate and fell isolated individual trees.

This spatial dispersion drastically increases extraction costs per trunk compared to temperate coniferous forests.

Key Concept

Heterogeneity of Equatorial Rainforest Species

Estimated Time:1m 0s

Question 13711Question →

Treasury Certificates are short- to medium-term money market instruments issued by the Central Bank on behalf of the government, with maturity periods typically ranging between one and two years.

True

False

Show answer & explanation

Answer: True

Answer

The statement is true because Treasury Certificates are money market debt instruments issued by the Central Bank for government borrowing, with maturity periods typically between one and two years.

The statement accurately reflects the definition and tenure of Treasury Certificates in Commerce. They are issued by the Central Bank to meet government funding needs for periods spanning one to two years.

Step-by-Step Solution

1

Identify the issuing authority and financial market segment for Treasury Certificates.

Treasury Certificates are issued by the Central Bank on behalf of the government within the money market.

Money markets deal with short- to medium-term credit instruments used by governments and financial institutions.

2

Analyze the maturity period of Treasury Certificates relative to other government instruments.

Treasury Certificates have a maturity period of 1 to 2 years, bridging very short-term Treasury Bills (under 1 year) and long-term Development Stocks.

Understanding maturity profiles helps distinguish between various government financial market instruments.

Key Concept

Characteristics and maturity duration of Treasury Certificates in the money market

Estimated Time:1m 0s

Question 13712Question →

Chief Okon contracted to purchase 100 bags of rice from a commodity supplier. Upon delivery, the supplier delivered a total of 120 bags. Under the provisions of the Sale of Goods Act regarding the delivery of a wrong quantity, which of the following correctly states Chief Okon's statutory options?

He may accept the 100 bags ordered and reject the remaining 20, accept all 120 bags paying for the excess at the contract rate, or reject the entire delivery.

He is legally obligated to retain all 120 bags but may demand a mandatory discount on the extra 20 bags.

He must accept only the exact 100 bags ordered and forfeits any legal right to accept the excess or reject the whole consignment.

He must automatically treat the contract as repudiated and can only sue the seller for breach of warranty.

Show answer & explanation

Answer: He may accept the 100 bags ordered and reject the remaining 20, accept all 120 bags paying for the excess at the contract rate, or reject the entire delivery.

Answer

The buyer may accept the 100 bags ordered and reject the remaining 20, accept all 120 bags paying for the excess at the contract rate, or reject the entire delivery.

According to the Sale of Goods Act (Section 30), where the seller delivers a quantity of goods larger than contracted, the buyer is given three clear choices: accept the contracted amount and reject the remainder, accept the entire delivery and pay for the excess at the contract rate, or reject the whole delivery.

Step-by-Step Solution

1

Identify the legal context and specific statutory provision.

The scenario concerns delivery of a larger quantity of goods than agreed under the Sale of Goods Act.

The seller supplied 120 bags instead of the contracted 100 bags.

2

Apply the statutory rule for delivery of excess goods.

The buyer has three legal options: (1) accept the contract quantity (100) and reject the rest (20), (2) accept all (120) and pay for the excess at the contract rate, or (3) reject the entire consignment (120).

Section 30 of the Sale of Goods Act grants the buyer full flexibility to accept in part, accept in full, or reject completely when excess quantity is tendered.

Key Concept

Delivery of Wrong Quantity (Excess Delivery) under the Sale of Goods Act

Question 13713Question →

Arrange the following sequential stages in the progressive marine erosion of a rocky headland, from the initial concentration of wave energy to its final reduced landform.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence of headland erosion begins with the formation of a sea cave, followed by its evolution into a sea arch, the collapse of the arch roof into a sea stack, and the final degradation of the stack into a sea stump.

Headland erosion follows a predictable geomorphic sequence: wave action exploits joints to form a sea cave, which enlarges into a sea arch. Subaerial weathering and gravity cause the arch roof to collapse into a detached sea stack, which is finally undercut by waves to leave a sea stump.

Step-by-Step Solution

1

Identify the initial erosional feature created where waves attack lines of weakness along a cliff base.

Marine forces excavate lines of structural weakness to produce a sea cave.

Hydraulic action and abrasion act first on weak joints at sea level.

2

Determine the landform created when wave erosion breaches completely through the headland.

The cave opens up through the headland, creating a sea arch.

Erosion from both sides of the headland meets or drives entirely through the wall.

3

Analyze the structural collapse of the unsupported arch roof due to subaerial processes and gravity.

The arch roof falls, leaving an isolated vertical column known as a sea stack.

Weathering destabilizes the roof, isolating the outer wall from the mainland.

4

Trace the final marine undercutting of the isolated pillar.

Wave action undercuts the base of the pillar, reducing it to a low sea stump.

Direct wave energy at the base destabilizes the stack until only a low remnant remains.

Key Concept

Sequential evolution of erosional coastal landforms on rocky headlands

Estimated Time:1m 0s

Question 13714Question →

A sinusoidal progressive wave propagating through an elastic medium is described by the equation $y = 0.04 \sin(60\pi t - 4\pi x)$ , where $x$ and $y$ are in meters and $t$ is in seconds. As the wave enters a second medium, its wave speed increases by $50\%$ . What is the wavelength of the wave in the second medium?

0.33\text{ m}

0.50\text{ m}

0.75\text{ m}

1.50\text{ m}

Show answer & explanation

Answer: $0.75\text{ m}$

Answer

The wavelength of the wave in the second medium is

0.75\text{ m}

.

Comparing

y = 0.04 \sin(60\pi t - 4\pi x)

to the standard wave equation

y = A \sin(\omega t - k x)

gives

\omega = 60\pi\text{ rad/s}

and

k = 4\pi\text{ rad/m}

. The source frequency is

f = \frac{\omega}{2\pi} = 30\text{ Hz}

, and the initial wavelength is

\lambda_1 = \frac{2\pi}{k} = 0.50\text{ m}

. The initial wave speed is

v_1 = \frac{\omega}{k} = 15\text{ m/s}

. When the wave enters the second medium, its speed increases by

50\%

to

v_2 = 22.5\text{ m/s}

. Frequency is a source property and remains constant (

30\text{ Hz}

) across media boundaries, so the new wavelength becomes

\lambda_2 = \frac{v_2}{f} = \frac{22.5}{30} = 0.75\text{ m}

.

Step-by-Step Solution

1

Extract angular frequency and wave number from the progressive wave equation.

From

y = 0.04 \sin(60\pi t - 4\pi x)

, we find

\omega = 60\pi\text{ rad/s}

and

k = 4\pi\text{ rad/m}

.

Standard form of a harmonic progressive wave is

y = A \sin(\omega t - k x)

.

2

Calculate the frequency and initial wavelength in the first medium.

Frequency

f = \frac{\omega}{2\pi} = \frac{60\pi}{2\pi} = 30\text{ Hz}

. Initial wavelength

\lambda_1 = \frac{2\pi}{k} = \frac{2\pi}{4\pi} = 0.50\text{ m}

.

Wave frequency and wavelength are related to angular parameters by

\omega = 2\pi f

and

k = \frac{2\pi}{\lambda}

.

3

Determine the initial wave speed and the new speed in the second medium.

Initial speed

v_1 = f \lambda_1 = 30 \times 0.50 = 15\text{ m/s}

. New speed

v_2 = 15 \times (1 + 0.50) = 22.5\text{ m/s}

.

Wave speed increases by

50\%

upon entering the second medium.

4

Apply boundary condition for wave refraction to determine the new wavelength.

Since frequency is invariant across media boundaries (

f_2 = f_1 = 30\text{ Hz}

),

\lambda_2 = \frac{v_2}{f_2} = \frac{22.5}{30} = 0.75\text{ m}

.

Frequency depends solely on the wave source and does not change when passing between media.

Key Concept

Frequency invariance and wavelength alteration across media boundaries in progressive waves

Question 13715Question →

During a flood monitoring operation along the Benue River basin, hydrologists require satellite imagery that can penetrate dense cloud cover and function effectively during both day and night. Which remote sensing system is most suitable for this task?

Active microwave radar remote sensing

Passive optical multispectral sensing

Thermal infrared radiometry

Panchromatic aerial photographic survey

Show answer & explanation

Answer: Active microwave radar remote sensing

Answer

Active microwave radar remote sensing is the most suitable system because radar operates at long electromagnetic wavelengths that penetrate clouds and rain, and active sensors supply their own illumination allowing night-time imaging.

Active microwave radar remote sensing uses synthetic aperture radar (SAR) or similar active instruments that generate their own radiation in the microwave portion of the spectrum. Long microwave signals penetrate cloud cover, fog, and rain, while self-illumination allows data acquisition regardless of daylight.

Step-by-Step Solution

1

Analyze the operational constraints specified in the scenario.

Identified key requirements: cloud penetration and round-the-clock (day/night) imaging capacity.

Selecting an appropriate remote sensing sensor requires matching environmental conditions with sensor spectral bands and energy sources.

2

Evaluate sensor energy source types (active vs. passive).

Active sensors emit their own energy pulses and do not depend on solar radiation, enabling night operation.

Passive sensors relying on reflected solar radiation cannot acquire data at night.

3

Evaluate atmospheric penetration across spectral bands.

Microwave wavelengths (1 mm to 1 m) easily pass through atmospheric cloud droplets and precipitation particles.

Shorter visible and infrared wavelengths suffer severe atmospheric scattering and absorption by clouds.

Key Concept

Active vs. Passive Remote Sensing and Microwave Atmospheric Transmission

Question 13716Question →

A uniform copper wire with a cross-sectional area of $2.0 \times 10^{-6}\,\text{m}^2$ carries a steady electric current of $4.0\,\text{A}$ . Given that the free electron density of copper is $2.5 \times 10^{28}\,\text{m}^{-3}$ and the elementary charge is $1.6 \times 10^{-19}\,\text{C}$ , calculate the drift velocity of the electrons in the wire in $\text{m/s}$ .

Show answer & explanation

Answer: 0.0005

Answer

The drift velocity of the electrons in the wire is

0.0005\,\text{m/s}

(or

5.0 \times 10^{-4}\,\text{m/s}

).

Applying the formula

I = n A e v_d

and solving for drift velocity yields

v_d = \frac{I}{n A e} = \frac{4.0}{(2.5 \times 10^{28})(2.0 \times 10^{-6})(1.6 \times 10^{-19})} = \frac{4.0}{8000} = 0.0005\,\text{m/s}

.

Step-by-Step Solution

1

State the formula relating electric current to microscopic drift velocity.

I = n A e v_d

Electric current is the net charge flowing per unit time across a conductor's cross-section.

2

Isolate the drift velocity

v_d

as the target variable.

v_d = \frac{I}{n A e}

Algebraic rearrangement places all known quantities on the right-hand side.

3

Substitute the numerical values into the equation.

v_d = \frac{4.0}{(2.5 \times 10^{28})(2.0 \times 10^{-6})(1.6 \times 10^{-19})}

Inserting

I = 4.0\,\text{A}

,

n = 2.5 \times 10^{28}\,\text{m}^{-3}

,

A = 2.0 \times 10^{-6}\,\text{m}^2

, and

e = 1.6 \times 10^{-19}\,\text{C}

.

4

Evaluate the arithmetic computation.

v_d = 0.0005\,\text{m/s}

Dividing

4.0

by

8000

yields

0.0005\,\text{m/s}

.

Key Concept

Relationship between electric current, charge carrier density, and drift velocity

Question 13717Question →

A sealed rigid glass bulb contains a fixed mass of helium gas at an initial pressure of $1.20 \times 10^5\text{ Pa}$ and a temperature of $27^\circ\text{C}$ . Assuming the volume of the bulb remains constant, calculate the final pressure of the gas in $\text{Pa}$ when it is heated to $127^\circ\text{C}$ .

Show answer & explanation

Answer: 160000

Answer

The final pressure of the gas is

1.60 \times 10^5\text{ Pa}

(

160\,000\text{ Pa}

).

The correct result of

160\,000\text{ Pa}

(

1.60 \times 10^5\text{ Pa}

) is obtained by applying the Pressure Law

\frac{P_1}{T_1} = \frac{P_2}{T_2}

using absolute temperatures (

T_1 = 300\text{ K}

,

T_2 = 400\text{ K}

).

Step-by-Step Solution

1

Convert the initial and final temperatures from degrees Celsius to the absolute temperature scale (Kelvin).

T_1 = 27 + 273 = 300\text{ K}

and

T_2 = 127 + 273 = 400\text{ K}

.

All gas law equations require absolute temperatures in Kelvin.

2

Apply the Pressure Law (Gay-Lussac's Law) for a fixed mass of gas at constant volume.

\frac{P_1}{T_1} = \frac{P_2}{T_2} \implies P_2 = P_1 \times \frac{T_2}{T_1}

The pressure of a gas is directly proportional to its absolute temperature when volume remains constant.

3

Substitute the known values to find

P_2

.

P_2 = 1.20 \times 10^5\text{ Pa} \times \frac{400\text{ K}}{300\text{ K}} = 1.60 \times 10^5\text{ Pa} = 160\,000\text{ Pa}

.

Multiplying

1.20 \times 10^5

by the temperature ratio

\frac{4}{3}

gives

1.60 \times 10^5\text{ Pa}

.

Key Concept

Pressure Law (Gay-Lussac's Law) and absolute temperature conversion

Question 13718Question →

The Copperbelt region spanning northern Zambia and the Katanga province of the Democratic Republic of Congo exhibits a remarkably high population density compared to the surrounding sparsely populated miombo woodland ecosystem of Central Africa. Which of the following factors primarily accounts for this concentrated population pattern?

Extensive mineral resource exploitation and associated urban-industrial infrastructure

High agricultural carrying capacity supported by fertile alluvial soils of major river basins

Severe coastal soil degradation acting as a push factor driving rural populations into interior forests

A low demographic dependency ratio driven by high infant mortality rates across rural communities

Show answer & explanation

Answer: Extensive mineral resource exploitation and associated urban-industrial infrastructure

Answer

Extensive mineral resource exploitation and associated urban-industrial infrastructure

The Copperbelt of Zambia and the Katanga region of the Democratic Republic of Congo represent a primary example of resource-anchored population concentration in Africa. Discovery and large-scale exploitation of rich copper and cobalt deposits led to urban-industrial growth, transport development, and massive labor migration into what was previously a sparsely settled environment.

Step-by-Step Solution

1

Identify the geographical zone and demographic anomaly described in the stem.

The target area is the Zambia-DRC Copperbelt within Central Africa, which exhibits an isolated high population density node in an otherwise low-density woodland zone.

Locating spatial demographic anomalies helps identify localized economic or physical drivers.

2

Analyze the primary economic driver of the Copperbelt.

The region contains vast deposits of copper and cobalt, which triggered industrial mining development, urbanization, and employment-driven in-migration.

Mineral resources act as major human economic pull factors altering natural regional population distribution.

3

Evaluate the choices to select the primary cause while eliminating false drivers.

Mineral exploitation and industrialization directly explain the high density, whereas farming, coastal push factors, or demographic ratios are incorrect explanations.

Distinguishing between mineral economic pull factors and agricultural or physical drivers ensures correct identification.

Key Concept

Impact of Mineral Resource Exploitation on Population Distribution and Urban Clusters in Africa

Question 13719Question →

A merchant receives goods from a supplier, identifies billing discrepancies alongside defective items, and subsequently settles the corrected account balance. Arrange the commercial documents generated during this billing adjustment and settlement phase in their correct chronological order of issuance.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct chronological order of issuance is Invoice, followed by Credit Note, then Statement of Account, and finally Official Receipt.

The sequence begins with the Invoice, which creates the initial bill for the buyer. Next, the Credit Note is issued to rectify overcharges or damaged goods by crediting the buyer's account. Following these adjustments, the seller issues the Statement of Account to summarize all debits and credits, presenting the net amount due. Finally, upon receiving payment, the seller issues an Official Receipt to confirm settlement of the account.

Step-by-Step Solution

1

Identify the initial document that creates the financial record for the transaction.

The Invoice is issued first by the seller to detail the items delivered and state the total charge.

An account balance cannot be adjusted or paid until an initial bill exists.

2

Determine the corrective document issued when errors or returned goods occur.

The Credit Note is issued next to adjust the buyer's account for damaged goods or overbilling.

A credit note reduces an existing charge billed on a previously issued invoice.

3

Identify the document that consolidates all debits and credits for payment.

The Statement of Account is compiled and sent by the seller summarizing total purchases, credits applied, and net balance owed.

The statement must incorporate both the initial invoice debits and credit note deductions before presenting the final amount due.

4

Identify the document that completes the transaction upon payment.

The Official Receipt is issued last once payment has been received.

The receipt serves as conclusive evidence that the outstanding debt summarized in the statement of account has been paid.

Key Concept

Chronological sequence of financial adjustments and account settlement documents in home trade

Estimated Time:1m 30s

Question 13720Question →

A group of small-scale traders in a local market forms a rotating savings association (Esusu) where each member contributes a fixed monthly amount that is paid to one member in rotation. Which of the following constitutes a major structural limitation of this traditional financial system compared to formal non-bank financial institutions?

It lacks formal legal framework and regulatory mechanism to enforce compliance or recover funds in case of default.

It is legally restricted from investing members' pooled contributions into productive commercial activities.

It is mandated by law to maintain a minimum liquidity reserve ratio with the Central Bank.

It expands total money supply within the economy by issuing cheque books to its members.

Show answer & explanation

Answer: It lacks formal legal framework and regulatory mechanism to enforce compliance or recover funds in case of default.

Answer

The main structural limitation of traditional financial systems like Esusu is that they lack a formal legal framework and statutory regulatory mechanism to enforce compliance or legally recover funds when a member defaults.

Traditional financial arrangements, such as rotating credit associations (Esusu), rely on social cohesion and mutual trust rather than formal legal contracts. If a member defaults after collecting their pool, the group lacks statutory regulatory mechanisms or legal instruments to recover the money.

Step-by-Step Solution

1

Analyze the operational framework of traditional financial systems (e.g., Esusu/Adashi).

Recognize that traditional systems operate informally based on custom, personal relationships, and social trust.

Understanding the basis of traditional credit schemes helps identify their vulnerabilities.

2

Compare traditional systems with formal non-bank financial institutions.

Formal institutions operate under statutory regulation (such as corporate laws and oversight bodies), offering legal protection to depositors.

Differentiating informal arrangements from statutory financial entities highlights legal and operational boundaries.

3

Identify the main limitation resulting from this informal structure.

In cases of fraud or default, members cannot rely on regulatory financial bodies or straightforward legal recourse to recover funds.

Absence of legal backing and institutional regulation is the fundamental drawdown of traditional credit pooling.

Key Concept

Operational characteristics and limitations of traditional financial systems (Esusu/Adashi) versus formal non-bank financial institutions.

Estimated Time:1m 15s

Answer

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