All practice questions

Question 13861Question →

A chemical balance is used to determine the mass of a metallic sphere, giving a reading of $6.0\text{ kg}$ . The sphere is then suspended from a spring balance at a laboratory where the local acceleration due to gravity is $10\text{ m s}^{-2}$ . If the spring balance reads $-3.0\text{ N}$ before any load is attached, what is the indicated reading on the spring balance when the sphere is suspended?

57.0\text{ N}

63.0\text{ N}

60.0\text{ N}

6.0\text{ N}

Show answer & explanation

Answer: $57.0\text{ N}$

Answer

The indicated reading on the spring balance is

57.0\text{ N}

.

The true weight of the metallic sphere is calculated as

W = mg = 6.0\text{ kg} \times 10\text{ m s}^{-2} = 60.0\text{ N}

. Because the spring balance has an initial zero reading of

-3.0\text{ N}

before any load is attached, the indicated reading when the sphere is hung is

60.0\text{ N} - 3.0\text{ N} = 57.0\text{ N}

.

Step-by-Step Solution

1

Calculate the true weight of the metallic sphere

W = mg = 6.0\text{ kg} \times 10\text{ m s}^{-2} = 60.0\text{ N}

Weight is the gravitational force acting on mass.

2

Set up the zero error relationship for instrument measurement

\text{Actual Weight} = \text{Indicated Reading} - \text{Zero Reading}

The actual physical value equals the observed pointer reading minus the zero reading of the unloaded instrument.

3

Substitute known values and solve for the indicated reading (

R

)

60.0\text{ N} = R - (-3.0\text{ N}) \implies R = 60.0 - 3.0 = 57.0\text{ N}

Solving the linear relation yields an indicated pointer position of

57.0\text{ N}

.

Key Concept

Mass versus Weight Measurement and Zero Error Correction

Estimated Time:1m 0s

Question 13862Question →

In an industrial non-destructive testing setup, an X-ray tube produces continuous X-radiation with a minimum cut-off wavelength of $3.3 \times 10^{-11}\text{ m}$ . What is the operating accelerating potential difference of the tube in kilovolts ( $\text{kV}$ )? (Take Planck's constant $h = 6.6 \times 10^{-34}\text{ J s}$ , speed of light $c = 3.0 \times 10^8\text{ m s}^{-1}$ , and electron charge $e = 1.6 \times 10^{-19}\text{ C}$ ).

Show answer & explanation

Answer: 37.5

Answer

The operating accelerating potential difference of the tube is 37.5 kV.

According to the Duane-Hunt law, the maximum kinetic energy of electrons hitting the target equal the maximum photon energy produced:

e V = h f_{\text{max}} = \frac{h c}{\lambda_{\text{min}}}

. Rearranging to solve for voltage gives

V = \frac{h c}{e \lambda_{\text{min}}}

. Substituting

h = 6.6 \times 10^{-34}\text{ J s}

,

c = 3.0 \times 10^8\text{ m s}^{-1}

,

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

, and

\lambda_{\text{min}} = 3.3 \times 10^{-11}\text{ m}

yields

V = 37,500\text{ V}

, which equals

37.5\text{ kV}

.

Step-by-Step Solution

1

Relate the maximum electron kinetic energy to the shortest X-ray photon wavelength using Duane-Hunt law

e V = E_{\text{max}} = \frac{h c}{\lambda_{\text{min}}}

At the Duane-Hunt cutoff limit, the entire kinetic energy of an accelerating electron is converted into a single X-ray photon.

2

Rearrange the equation to solve for the accelerating voltage

V

V = \frac{h c}{e \lambda_{\text{min}}}

Isolating

V

allows direct calculation from known fundamental constants and the given minimum wavelength.

3

Substitute the physical constants and calculate the value of

V

in Volts

V = \frac{(6.6 \times 10^{-34}\text{ J s})(3.0 \times 10^8\text{ m s}^{-1})}{(1.6 \times 10^{-19}\text{ C})(3.3 \times 10^{-11}\text{ m})} = 37,500\text{ V}

Carrying out arithmetic with scientific notation powers yields

3.75 \times 10^4\text{ V}

.

4

Convert the potential difference from Volts (V) to kilovolts (kV)

37,500\text{ V} = 37.5\text{ kV}

Dividing by 1000 converts potential difference into the requested kilovolt unit.

Key Concept

Duane-Hunt Law and Cut-off Wavelength in X-ray Production

Question 13863Question →

An atom has three stationary energy levels given by $E_1 = -12.50\text{ eV}$ , $E_2 = -6.80\text{ eV}$ , and $E_3 = -3.50\text{ eV}$ . What is the wavelength, in nanometers ( $\text{nm}$ ), of the photon emitted during the transition that produces the longest wavelength line in its emission spectrum? (Take Planck's constant $h = 6.6 \times 10^{-34}\text{ J}\cdot\text{s}$ , speed of light $c = 3.0 \times 10^8\text{ m/s}$ , and $1\text{ eV} = 1.6 \times 10^{-19}\text{ J}$ )

Show answer & explanation

Answer: 375

Answer

The wavelength of the photon emitted for the longest wavelength spectral line is 375 nm.

Photon wavelength is related to transition energy by

\lambda = \frac{hc}{\Delta E}

. To find the longest wavelength spectral line, the transition with the smallest energy gap must be used. Evaluating all emission transitions between the levels gives

\Delta E_{3 \to 2} = 3.30\text{ eV}

,

\Delta E_{2 \to 1} = 5.70\text{ eV}

, and

\Delta E_{3 \to 1} = 9.00\text{ eV}

. The minimum energy difference is

3.30\text{ eV}

. Converting

3.30\text{ eV}

to Joules gives

3.30 \times 1.6 \times 10^{-19} = 5.28 \times 10^{-19}\text{ J}

. Substituting this into the wavelength formula yields

\lambda = \frac{6.6 \times 10^{-34} \times 3.0 \times 10^8}{5.28 \times 10^{-19}} = 3.75 \times 10^{-7}\text{ m} = 375\text{ nm}

.

Step-by-Step Solution

1

Determine which electronic transition yields the longest wavelength photon.

Transition from

E_3

to

E_2

yields the minimum energy difference of

3.30\text{ eV}

.

Since

\lambda = \frac{hc}{\Delta E}

, the longest wavelength corresponds to the smallest energy transition.

2

Convert the transition energy from electron-volts to Joules.

\Delta E = 5.28 \times 10^{-19}\text{ J}

.

SI units are required for calculations involving Planck's constant and the speed of light.

3

Calculate the wavelength

\lambda

using the photon energy formula

\lambda = \frac{hc}{\Delta E}

.

\lambda = 375\text{ nm}

.

Substituting

h = 6.6 \times 10^{-34}\text{ J}\cdot\text{s}

,

c = 3.0 \times 10^8\text{ m/s}

, and

\Delta E = 5.28 \times 10^{-19}\text{ J}

gives

3.75 \times 10^{-7}\text{ m}

, which equals

375\text{ nm}

.

Key Concept

Inverse relationship between transition energy and photon wavelength in atomic emission spectra

Question 13864Question →

A commercial bank applies for ₦2 billion property insurance coverage for its nationwide vault network. Meridian Assurance evaluates the financial risk involved, determines the premium rate, and sets the policy terms before issuing the cover. Which of the following functions is Meridian Assurance performing in this process?

Underwriting

Co-insurance

Reinsurance

Indemnity

Show answer & explanation

Answer: Underwriting

Answer

Underwriting

Underwriting is the fundamental insurance procedure wherein an insurer examines a proposed risk, evaluates the likelihood of a claim, determines terms and conditions, and calculates the appropriate premium before agreeing to cover the risk.

Step-by-Step Solution

1

Analyze the action performed by Meridian Assurance in the scenario.

Meridian Assurance is evaluating the risk, determining the premium rate, and setting policy conditions for the applicant.

Identifying the core operational activity described in the stem is required to select the correct insurance concept.

2

Match the identified activity to the standard insurance definitions.

The process of assessing risk, deciding on acceptability, and fixing premium terms is defined as underwriting.

Underwriting directly describes the evaluation and pricing phase conducted by an insurer prior to issuing coverage.

Key Concept

Underwriting

Question 13865Question →

Starting from the southern Atlantic coastline and moving northwards toward the northern border of Nigeria, arrange the following agricultural production belts in their correct latitudinal sequence from south to north.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from south to north is: Coastal Belt (oil palm and rubber) → High Forest Belt (cocoa and timber) → Guinea Savanna / Middle Belt (yam, cassava, and maize) → Sudan and Sahel Savanna Belt (millet, sorghum, groundnut, and cattle pastoralism).

Agricultural production systems in Nigeria are primarily controlled by the south-to-north latitudinal rainfall gradient. Annual rainfall decreases from over

3,000\text{ mm}

at the coast to less than

500\text{ mm}

near the northern border. Consequently, agricultural land use progresses from coastal wetland and oil palm production, to rainforest tree-crop farming (cocoa/rubber), through the Middle Belt root-and-grain transition zone, to the northern dry savanna grain and pastoralism belt.

Step-by-Step Solution

1

Identify the southernmost coastal agro-ecological zone.

The coastal swamp forest region receives the highest rainfall (

>2,500\text{ mm}

) and supports water-loving perennials like oil palm, rubber, and swamp rice.

Rainfall amount and duration decrease progressively from the Atlantic coast inland toward the northern boundary.

2

Determine the intermediate forest crop belt.

Moving inland into the tropical rainforest belt, cocoa and timber plantations predominate.

Cocoa requires high temperatures and moderate-to-high rainfall with a short dry period.

3

Locate the Middle Belt transition zone.

The Guinea Savanna features a single-peak or moderate rainfall regime ideal for grain-tuber mixed farming (yam, cassava, maize).

This region serves as the major food basket separating forest tree-crop zones from northern grain zones.

4

Identify the northernmost agricultural and pastoral belt.

The Sudan and Sahel savannas in the far north support millet, sorghum, groundnuts, and nomadic pastoralism.

Short rainy seasons (

3-5

months) and low humidity restrict crop production to drought-resistant cereals and favor livestock rearing due to low tsetse fly infestation.

Key Concept

Latitudinal Zonation of Agricultural Systems in Nigeria

Question 13866Question →

A country experiencing a persistent deficit in its visible trade account develops international eco-tourism projects and cultural heritage festivals to attract foreign visitors. How does this policy directly assist in improving the country's overall balance of payments position?

It generates foreign currency receipts recorded as invisible export earnings.

It converts service earnings into tangible merchandise export figures in the balance of trade.

It shifts commercial hospitality operations into non-commercial direct personal services.

It automatically reduces customs tariff rates applied to imported consumer goods.

Show answer & explanation

Answer: It generates foreign currency receipts recorded as invisible export earnings.

Answer

It generates foreign currency receipts recorded as invisible export earnings.

When international tourists spend money within a host country on accommodation, transport, and recreation, foreign exchange flows into the country. Because these earnings stem from services rather than physical goods, they are classified as invisible exports, directly strengthening the current account of the balance of payments.

Step-by-Step Solution

1

Analyze how foreign tourist spending impacts host country transactions.

Foreign tourists spend money on accommodation, dining, guided tours, and local transport.

These expenditures represent payments by foreign residents for locally provided services.

2

Classify these service transactions within international trade accounting.

The foreign currency inflow is categorized under invisible exports in the current account of the balance of payments.

Although no physical merchandise is shipped abroad, providing services to non-residents earns foreign exchange that helps offset visible trade deficits.

Key Concept

Tourism as an Invisible Export in Balance of Payments

Question 13867Question →

Match each world climate type on the left with its defining seasonal atmospheric and precipitation characteristics on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Mediterranean climate matches winter cyclonic rainfall with summer drought; Tropical monsoon climate matches onshore wind reversal with heavy seasonal rainfall; Mid-latitude steppe climate matches semi-arid continental conditions with high temperature range; Subarctic climate matches prolonged severe freezing winters with extreme annual thermal amplitude.

Each climate type correctly maps to its characteristic temperature and precipitation regime: Mediterranean climates experience dry summers and wet winters; Tropical monsoon climates exhibit wind reversal rainfall with a short dry period; Mid-latitude steppes are semi-arid with wide temperature ranges; Subarctic climates have prolonged freezing winters with extreme annual thermal amplitude.

Step-by-Step Solution

1

Identify the primary atmospheric controls for the Mediterranean (

Cs

) climate

Matched with winter westerlies rainfall and summer subtropical high subsidence.

Seasonal migration of pressure belts brings dry horse latitude conditions in summer and polar front low-pressure systems in winter.

2

Analyze the wind reversal mechanism of Tropical Monsoon (

Am

) climate

Matched with onshore seasonal wind reversal and high total precipitation despite a short dry season.

Differential heating of land and sea causes seasonal monsoonal wind shifts that bring intense wet seasons.

3

Distinguish between continental interior climate regimes (

BSk

and

Dfc

)

Matched

BSk

with semi-arid steppe grasslands and

Dfc

with extreme subarctic long winter conditions.

Distance from oceans reduces precipitation in steppes, while high latitude continental locations produce extreme winter cooling in subarctic zones.

Key Concept

Köppen Climate Classification and Seasonal Air Mass Controls

Question 13868Question →

Match each coastal marine process or wave phenomenon listed in the left column with its corresponding geomorphic action or landform effect in the right column.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Constructive wave action matches deposition of marine sediment building broad beaches; Hydraulic action matches pneumatic pressure from trapped air compressed in cliff fissures; Wave refraction matches bending of wave fronts concentrating energy on headlands; Corrasion (Abrasion) matches scouring and scraping of cliff bases using wave-borne sediment.

Constructive wave action deposits sediment to build beaches because swash exceeds backwash. Hydraulic action exerts pneumatic pressure as air is compressed in cliff cracks. Wave refraction bends waves to focus erosive power on projecting headlands. Corrasion utilizes sand and pebbles as abrasive tools to scour cliff bases.

Step-by-Step Solution

1

Analyze constructive wave dynamics.

Swash dominates over backwash, leading directly to sediment deposition.

Low-frequency, low-energy waves transport material onto the shore faster than it is pulled back into the ocean.

2

Examine the mechanics of hydraulic action.

Identify trapped air compression inside rock joints.

The force of moving water compresses trapped pockets of air in rock cavities, exerting tremendous pressure that shatters jointed cliffs.

3

Evaluate wave refraction along irregular coastlines.

Determine that wave crests curve toward headlands.

Friction in shallow water near headlands slows down wave segments while deeper segments in bays continue faster, redirecting energy.

4

Identify the process of corrasion (abrasion).

Connect wave-carried load to cliff base erosion.

Sediments hurled by waves act like sandpaper, scouring away rock faces near high-tide level.

Key Concept

Coastal wave processes and marine erosional/depositional mechanics

Question 13869Question →

Match each geographical region of Nigeria listed on the left with its corresponding population density pattern and primary geographic driver on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Kano Close-Settled Zone matches high rural-urban density sustained by intensive manuring and trans-Saharan trade; Middle Belt (Borgu/Kontagora) matches sparse population density caused by slave-raiding, leached soils, and tsetse flies; Niger Delta Coastal Fringe matches linear settlement morphology constrained to dry natural levees; Southeastern Igbo Heartland matches extremely high rural population density driven by oil palm cultivation.

Each region's demographic density and settlement layout reflect a distinct combination of environmental features and historical factors: northern close-settled zones rely on intensive land care and trade; the Middle Belt suffered historical depopulation and vector diseases; coastal deltas constrain layout along levees; and the southeastern palm belt supports dense rural populations on arable land.

Step-by-Step Solution

1

Analyze the northern agricultural zone.

Kano Close-Settled Zone is famous for intensive farming (manuring) around urban centers.

Identify the ecological and historical driver for northern high-density pockets.

2

Analyze the central belt of Nigeria.

The Middle Belt (Borgu/Kontagora) is a known low-density belt influenced by tsetse flies and historical slave raids.

Distinguish between physical constraints and historical factors shaping low density.

3

Examine coastal wetland settlement forms.

The Niger Delta coastal environment forces population alignment along dry levees.

Relate physical terrain to linear settlement morphology.

4

Examine southeastern population concentrations.

The Anambra-Imo axis has exceptionally high rural population density based on palm agricultural land use.

Recognize the unique rural high-density phenomenon of Southeastern Nigeria.

Key Concept

Regional variation of population density drivers and settlement morphology in Nigeria

Estimated Time:1m 30s

Question 13870Question →

The Northern Transport Corridor is a vital trade arterial network in East Africa connecting landlocked countries to international maritime trade. Arrange the following urban transit centers in geographical sequence along this corridor, starting from the coastal seaport gateway on the Indian Ocean and proceeding inland towards the landlocked interior.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct geographical sequence from the coastal maritime gateway to the landlocked interior along the Northern Transport Corridor is Mombasa, Nairobi, Kampala, and Kigali.

The Northern Transport Corridor begins at the seaport of Mombasa on the Indian Ocean in Kenya, proceeds inland through Nairobi, crosses into Uganda to reach Kampala, and extends further inland to Kigali in landlocked Rwanda.

Step-by-Step Solution

1

Identify the maritime trade entry point on the coast.

Mombasa is the starting coastal seaport on the Indian Ocean.

Maritime transit corridors originate at ocean ports where goods are discharged for inland distribution.

2

Trace the initial inland transport leg within the coastal state.

Cargo travels northwest along the highway/railway network to Nairobi.

Nairobi is Kenya's central inland transport and logistics node between the coast and the western borders.

3

Follow the corridor across the international border to the first landlocked country.

Goods enter Uganda and reach Kampala.

Kampala serves as the major transit and consumption center in landlocked East Africa.

4

Determine the furthest landlocked terminal destination among the items.

The corridor extends further west from Uganda into Rwanda to reach Kigali.

Landlocked Rwanda relies on transit through both Uganda and Kenya to access the Indian Ocean.

Key Concept

East African Trade Corridors and Hinterland Transport Connectivity

Question 13871Question →

A sand bag of mass $8.0\text{ kg}$ is suspended vertically by a light rope. A projectile of mass $0.50\text{ kg}$ moving horizontally at a speed of $170\text{ m s}^{-1}$ strikes the sand bag and becomes embedded in it. What is the common speed, in $\text{m s}^{-1}$ , of the sand bag and the embedded projectile immediately after collision?

Show answer & explanation

Answer: 10

Answer

The common speed of the sand bag and embedded projectile immediately after the collision is

10.0\text{ m s}^{-1}

.

According to the principle of conservation of linear momentum, total momentum before impact equals total momentum after impact. The initial momentum of the system is entirely from the projectile:

p_i = 0.50 \times 170 = 85\text{ kg m s}^{-1}

. After collision, both objects move together with a total mass of

0.50 + 8.0 = 8.5\text{ kg}

. Setting

8.5 v = 85

gives

v = 10\text{ m s}^{-1}

.

Step-by-Step Solution

1

State the conservation of linear momentum equation for an inelastic collision

m_1 u_1 + m_2 u_2 = (m_1 + m_2) v

Since no net external horizontal force acts on the system during impact, total linear momentum is conserved.

2

Substitute the given values into the momentum balance equation

(0.50\text{ kg})(170\text{ m s}^{-1}) + (8.0\text{ kg})(0\text{ m s}^{-1}) = (0.50\text{ kg} + 8.0\text{ kg}) v

The projectile embeds into the sand bag, so they move together with a single combined mass.

3

Solve the linear equation for the common final velocity

v

85 = 8.5 v \implies v = 10\text{ m s}^{-1}

Dividing total initial momentum by total combined mass yields the final speed.

Key Concept

Conservation of Linear Momentum in Completely Inelastic Collisions

Estimated Time:1m 30s

Question 13872Question →

A glass relative density bottle with linear expansivity $\alpha = 8.0 \times 10^{-6}\text{ K}^{-1}$ is completely filled with $204\text{ g}$ of a liquid at $15^\circ\text{C}$ . When heated to $65^\circ\text{C}$ , $4\text{ g}$ of the liquid overflows. What is the real cubic expansivity of the liquid?

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

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

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

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

Show answer & explanation

Answer: $4.24 \times 10^{-4}\text{ K}^{-1}$

Answer

The real cubic expansivity of the liquid is

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

.

The real cubic expansivity of a liquid accounts for both the apparent expansion observed as overflow and the expansion of the container itself. Calculating apparent cubic expansivity yields

\gamma_a = \frac{4\text{ g}}{200\text{ g} \times 50\text{ K}} = 4.0 \times 10^{-4}\text{ K}^{-1}

. Combining this with the glass bottle's cubic expansivity

\gamma_v = 3 \times 8.0 \times 10^{-6} = 0.24 \times 10^{-4}\text{ K}^{-1}

gives

\gamma_r = 4.24 \times 10^{-4}\text{ K}^{-1}

.

Step-by-Step Solution

1

Calculate the mass of liquid remaining in the bottle at the higher temperature.

m_{\text{remaining}} = 204\text{ g} - 4\text{ g} = 200\text{ g}

The apparent expansivity formula using the mass method requires the remaining mass of liquid that occupies the bottle volume at the elevated temperature.

2

Calculate the apparent cubic expansivity (

\gamma_a

) of the liquid.

\gamma_a = \frac{\text{mass expelled}}{m_{\text{remaining}} \times \Delta T} = \frac{4}{200 \times (65 - 15)} = \frac{4}{10000} = 4.0 \times 10^{-4}\text{ K}^{-1}

Apparent expansivity is defined as the mass of liquid expelled divided by the product of remaining mass and temperature rise.

3

Determine the cubic expansivity of the glass vessel (

\gamma_v

).

\gamma_v = 3\alpha = 3 \times (8.0 \times 10^{-6}\text{ K}^{-1}) = 2.4 \times 10^{-5}\text{ K}^{-1} = 0.24 \times 10^{-4}\text{ K}^{-1}

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

4

Calculate the real cubic expansivity of the liquid (

\gamma_r

).

\gamma_r = \gamma_a + \gamma_v = 4.0 \times 10^{-4}\text{ K}^{-1} + 0.24 \times 10^{-4}\text{ K}^{-1} = 4.24 \times 10^{-4}\text{ K}^{-1}

The real volume expansivity of a liquid equals the sum of its apparent expansivity and the cubic expansivity of its container.

Key Concept

Relationship between real cubic expansivity, apparent cubic expansivity, and vessel cubic expansivity (

\gamma_r = \gamma_a + \gamma_v

).

Estimated Time:1m 30s

Question 13873Question →

Under a holding company arrangement, a subsidiary company completely loses its distinct legal personality and ceases to exist as a separate corporate entity once majority voting shares are acquired.

True

False

Show answer & explanation

Answer: False

Answer

False

The statement is false because a subsidiary company continues to exist as a separate legal entity with its own legal rights, obligations, and financial records, despite being controlled by a holding company.

Step-by-Step Solution

1

Examine the legal structure of a holding-subsidiary company relationship.

A holding company owns a controlling portion (over 50%) of the equity shares in another company (the subsidiary).

Defining the ownership connection establishes legal rights and operational boundaries.

2

Differentiate between holding company control and complete corporate absorption.

In complete absorption or merger, the target firm is dissolved. In contrast, a subsidiary maintains its status as an independent legal entity capable of suing and being sued in its own name.

Separate legal personality is a defining characteristic of a subsidiary within a business combination.

Key Concept

Legal Independence of Subsidiary Companies

Question 13874Question →

A progressive wave traveling through a primary medium is described by the displacement equation $y = 0.05 \sin(80\pi t - 4\pi x)$ , where $x$ and $y$ are in meters and $t$ is in seconds. If the wave enters a secondary medium where its speed decreases to $15\text{ m s}^{-1}$ , what is the wavelength of the wave in the secondary medium?

0.375\text{ m}

0.500\text{ m}

0.188\text{ m}

2.667\text{ m}

Show answer & explanation

Answer: $0.375\text{ m}$

Answer

The wavelength of the wave in the secondary medium is

0.375\text{ m}

.

The option specifying

0.375\text{ m}

is correct because wave frequency

f

remains constant when moving between different media. Extracting

f = \frac{80\pi}{2\pi} = 40\text{ Hz}

from the initial equation allows direct calculation of the new wavelength using

\lambda_2 = \frac{v_2}{f} = \frac{15}{40} = 0.375\text{ m}

.

Step-by-Step Solution

1

Extract angular frequency and wavenumber from the wave equation

From

y = 0.05 \sin(80\pi t - 4\pi x)

, we identify

\omega = 80\pi\text{ rad s}^{-1}

and

k = 4\pi\text{ rad m}^{-1}

.

The standard wave equation form is

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

.

2

Determine the constant frequency of the wave

f = \frac{\omega}{2\pi} = \frac{80\pi}{2\pi} = 40\text{ Hz}

.

Frequency depends solely on the wave source and remains unchanged when crossing media boundaries.

3

Calculate the wavelength in the secondary medium using the new speed

\lambda_2 = \frac{v_2}{f} = \frac{15\text{ m s}^{-1}}{40\text{ Hz}} = 0.375\text{ m}

.

The wave speed formula

v = f \lambda

rearranged gives

\lambda = \frac{v}{f}

.

Key Concept

Wave speed changes across media boundaries while frequency remains invariant

Question 13875Question →

A sample of liquid has an initial volume of $500\text{ cm}^3$ inside a container at $20^\circ\text{C}$ . Upon heating the system to $70^\circ\text{C}$ , the liquid's apparent volume expansion is measured to be $10\text{ cm}^3$ . If the linear expansivity of the container material is $1.0 \times 10^{-5}\text{ K}^{-1}$ , what is the real cubic expansivity of the liquid?

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

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

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

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

Show answer & explanation

Answer: $4.3 \times 10^{-4}\text{ K}^{-1}$

Answer

The real cubic expansivity of the liquid is

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

.

The real cubic expansivity of a liquid equals the sum of its apparent cubic expansivity and the cubic expansivity of its vessel (

\gamma_r = \gamma_a + \gamma_v

). Calculating apparent cubic expansivity gives

\frac{10}{500 \times 50} = 4.0 \times 10^{-4}\text{ K}^{-1}

, and the container's cubic expansivity is

3 \times (1.0 \times 10^{-5}) = 0.3 \times 10^{-4}\text{ K}^{-1}

. Adding these yields

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

.

Step-by-Step Solution

1

Calculate the temperature change (

\Delta T

) and the apparent cubic expansivity (

\gamma_a

) of the liquid.

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

, so

\gamma_a = \frac{\Delta V_a}{V_0 \Delta T} = \frac{10}{500 \times 50} = 4.0 \times 10^{-4}\text{ K}^{-1}

.

Apparent expansivity relates apparent volume increase to initial volume and temperature change.

2

Convert the container's linear expansivity (

\alpha_v

) to its cubic expansivity (

\gamma_v

).

\gamma_v = 3\alpha_v = 3 \times (1.0 \times 10^{-5}\text{ K}^{-1}) = 3.0 \times 10^{-5}\text{ K}^{-1} = 0.3 \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

) using the relation

\gamma_r = \gamma_a + \gamma_v

.

\gamma_r = 4.0 \times 10^{-4}\text{ K}^{-1} + 0.3 \times 10^{-4}\text{ K}^{-1} = 4.3 \times 10^{-4}\text{ K}^{-1}

.

Real expansion of a liquid accounts for both its observed (apparent) expansion and the expansion of the containing vessel.

Key Concept

Relationship between real expansivity, apparent expansivity of liquids, and container expansivity

Estimated Time:1m 30s

Question 13876Question →

A bat emitting an ultrasonic sound pulse towards a flat vertical wall receives the reflected echo $0.12\text{ s}$ after emission. If the speed of sound in air is $340\text{ m/s}$ , what is the distance between the bat and the wall at the moment of emission?

20.4\text{ m}

40.8\text{ m}

81.6\text{ m}

10.2\text{ m}

Show answer & explanation

Answer: $20.4\text{ m}$

Answer

The distance between the bat and the wall is

20.4\text{ m}

.

The distance to the wall is

20.4\text{ m}

because sound undergoes a two-way journey (from source to reflector and back). Multiplying the speed of sound (

340\text{ m/s}

) by the total time (

0.12\text{ s}

) yields the round-trip distance of

40.8\text{ m}

. Dividing this value by

2

gives the one-way distance of

20.4\text{ m}

.

Step-by-Step Solution

1

Calculate the total distance traveled by the sound wave during the round trip.

d_{\text{total}} = v \times t = 340\text{ m/s} \times 0.12\text{ s} = 40.8\text{ m}

The sound wave travels from the bat to the obstacle and reflects back to the bat.

2

Divide the total round-trip distance by

2

to determine the one-way distance to the wall.

d = \frac{d_{\text{total}}}{2} = \frac{40.8\text{ m}}{2} = 20.4\text{ m}

An echo involves a two-way path, so the one-way distance is half the total distance covered by the wave.

Key Concept

Echo and Two-Way Distance Calculation

Estimated Time:1m 30s

Question 13877Question →

Guinea possesses one of the world's largest reserves of high-grade bauxite. Which geological process is primarily responsible for the formation and concentration of these extensive bauxite deposits across the country's plateau landscapes?

Deep chemical weathering and leaching of aluminum-rich rocks under humid tropical conditions

Sedimentation and compaction of organic plant debris in ancient low-lying lacustrine basins

Crystallization of minerals from magmatic intrusions within Precambrian basement complexes

Precipitation of dissolved salts following the complete evaporation of inland saline lakes

Show answer & explanation

Answer: Deep chemical weathering and leaching of aluminum-rich rocks under humid tropical conditions

Answer

Deep chemical weathering and leaching of aluminum-rich rocks under humid tropical conditions

Bauxite is a residual deposit created by deep chemical weathering (lateritization) under warm, wet tropical climates. Intense leaching washes away silica and alkali bases from aluminum-bearing parent rocks, leaving behind concentrated hydrous aluminum oxides on stable plateaus.

Step-by-Step Solution

1

Identify the mineral nature and formation environment of bauxite.

Bauxite is a residual ore composed chiefly of hydrous aluminum oxides.

It is not a primary igneous or sedimentary rock, but a product of weathered mantle rocks.

2

Analyze how tropical weathering concentrates aluminum minerals in Guinea.

High annual rainfall and warm temperatures accelerate lateritization.

Soluble compounds such as silica, calcium, and sodium are leached downward out of aluminum-bearing silicate parent rocks, leaving a residual crust of insoluble aluminum minerals on flat, stable plateaus.

Key Concept

Bauxite Formation and Tropical Lateritization in Africa

Estimated Time:1m 0s

Question 13878Question →

Commercial enterprises rely on insurance to mitigate risks and sustain economic growth. Match each role of insurance in commerce on the left with its corresponding operational benefit to business on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Provision of business continuity matches with absorbing accidental losses to ensure enterprise survival; Enhancement of credit rating for loans matches with providing financial security for bank credit facilities; Facilitation of foreign trade matches with protecting traders against marine hazards and payment risks; Creation of employment opportunities matches with generating career paths for insurance professionals.

Each role of insurance directly corresponds to a specific operational mechanism: preserving solvency maintains continuity, backing loans enhances creditworthiness, protecting ocean transport facilitates foreign trade, and staffing insurance firms generates employment.

Step-by-Step Solution

1

Identify the primary economic role of insurance in mitigating business operational risk.

Provision of business continuity matches the absorption of accidental losses to prevent insolvency.

Indemnity replaces lost assets and restores the business to its former financial position.

2

Analyze how insurance facilitates capital acquisition and financing.

Enhancement of credit rating for loans matches providing collateral confidence to commercial banks.

Lenders prefer lending against insured assets because the risk of loss is transferred to an insurer.

3

Examine how insurance aids international commercial transactions.

Facilitation of foreign trade matches protecting exporters and importers against marine cargo risks.

International commerce involves long distances and sea hazards best covered by marine and export credit insurance.

4

Determine the direct tertiary industry benefit of insurance.

Creation of employment opportunities matches providing professional career paths for underwriters and brokers.

Insurance operates as a major commercial sector employing various skilled personnel.

Key Concept

Role and Importance of Insurance in Business and Commerce

Question 13879Question →

Several independent commercial banks operating within the financial sector form an official organization to establish uniform codes of conduct, enforce ethical practices within their specific line of business, and collectively lobby the central monetary authorities on banking regulations. Which type of commercial organization has been created?

Trade association

Chamber of commerce

Trade union

Employers' association

Show answer & explanation

Answer: Trade association

Answer

Trade association

The correct answer is a trade association because the body is formed exclusively by firms operating within the same industry (banking) to promote their shared business interests, establish common operational guidelines, and engage in lobbying for that specific trade.

Step-by-Step Solution

1

Analyze the membership scope described in the scenario

The membership consists exclusively of firms (commercial banks) operating within a single line of business (the banking industry).

Structural scope distinguishes sector-specific bodies from geographically bounded multi-industry organizations.

2

Examine the primary functions performed by the body

The organization standardizes ethical practices, creates industry guidelines, and lobbies government authorities specifically for the banking sector.

These aims directly align with the core functions of a trade association representing a specific trade.

Key Concept

Structural and functional distinction of Trade Associations as single-industry business bodies

Question 13880Question →

Despite the formation of regional economic groupings such as ECOWAS, EAC, and SADC to foster regional integration, intra-African trade accounts for a relatively small percentage of the continent's total commerce. Which of the following factors represents the primary structural challenge hindering trade expansion among African nations?

Low economic complementarity among nations that predominantly export similar raw primary commodities

A strict prohibition on overland transport connectivity between ECOWAS and SADC member countries

The complete classification of all West African nations as landlocked states lacking maritime access

The existence of a unified single monetary currency legally binding across all African economic groupings

Show answer & explanation

Answer: Low economic complementarity among nations that predominantly export similar raw primary commodities

Answer

Low economic complementarity among nations that predominantly export similar raw primary commodities

The primary structural obstacle to intra-African trade is low economic complementarity. Because many African countries share similar ecological zones and resource endowments, they produce similar primary agricultural goods and mineral resources aimed at export markets outside Africa, rather than goods required by neighboring African economies.

Step-by-Step Solution

1

Analyze the production structures of African economies

Identified that a majority of African nations are primary producers exporting unprocessed minerals and agricultural goods to industrial nations in Europe, Asia, and North America.

Intra-regional trade relies on nations producing goods that neighboring nations need to import.

2

Evaluate the impact of commodity duplication on intra-regional trade

Concluded that because neighboring countries often produce identical raw items, mutual trading demand remains low (low economic complementarity).

Structural economic alignment is essential for high-volume trade between neighboring states.

Key Concept

Structural barriers and economic complementarity in intra-African trade

Answer

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