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Quiz 12 of 14

# 2015 Physics WAEC Theory Past Questions

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## Question 1

(a) What is a projectile?

A projectile is an object which can be fashioned to form a parabola. The trajectory of a projectile is usually parabolic or curvilinear.

(b) Give the reason why the horizontal component of the velocity of a projectile remains the same at every point of its flight.

- Zero air resistance
- Zero horizontal forces; hence no acceleration and no change in the velocity

## Question 2

A body is projected at an angle of 30oto the horizontal with a velocity of 150ms-1. Calculate the time it takes the greatest height. [Take g = 10ms-2 and neglect air resistance]

Given:
θ = 30o; u = 150ms-1; t = ? and g = 10ms-2
→ The time taken to reach maximum height, t =?

Recall that

t = $$\frac{usin \theta}{g}$$

t = $$\frac{150 \: \times \: sin 30^o}{10}$$

t = $$\frac{75}{10}$$

= 7.5s

## Question 3

A wire of length 2.00 m and radius 1.0 mm is stretched by 25.0 mm on the application of a force of 103 N. Calculate the Young's modulus for the wire.

Solution

Given:
L = 2m

r = 1mm = 1 x 10-3m

e = 25mm = 25 x 10-3m

F = 100oN

Young modules, E = $$\frac{Fl}{Ae}$$

Area, A = πr2 = 3.142 x (10-3)2 = 3.142 x 10-6

Young modules, E = $$\frac{Fl}{Ae}$$

= $$\frac{1000 \: \times \: 2.00}{3.142 \: \times \: 10^{-6} \: \times \: 25 \: \times \: 10^{-3}}$$

= $$\scriptsize 2.547 \: \times \: 10^{10} NM^{-2}$$

## Question 4

State three ways of increasing the rate of cooling of a cup of hot tea.

- Increasing the surface area by blowing

- Mixing

- Stirring

- Reducing the ambient temperature

## Question 5

(a) What is doping in a semi-conductor?

Doping in a semiconductor is the addition of impurities to a pure semiconductor to increase its electrical conductivity through an increase in the number of holes and electrons or charge carriers.

(b) Draw the symbol for OR gate.

## Question 6

(a) The circuit above consists of an a.c voltage input, a diode, a resistor, and a voltmeter. Identify the circuit.

The circuit is a half-wave rectifier

(b) Draw the waveform for the output voltage.

## Question 7

(a) Write the De Broglie equation.

De Broglie's equation is given as

$$\scriptsize \lambda = \normalsize \frac{h}{p} \\ \scriptsize = \normalsize\frac{h}{mv}$$

h = planck's constant

* It should be noted h = 6.63 x 1034Js
mass of the wave particle = m(in kg)
velocity of wave particle = v(in ms-1)
Momentum of wave particle = P(in kgms-1)

(b) Explain the significance of the equation

The significance of the equation is that it shows that matter has a dual nature, it can exist as a wave and as a particle.

## Question 8

(a) (i) Define uniform acceleration

Uniform acceleration is the acceleration of a body when it is undergoing a constant time rate of change in velocity.

(a) (ii) Write an equation that relates linear velocity, angular velocity and radius of path in circular motion.

V = wr

V = Linear/Tangential velocity
w = Angular velocity

Linear velocity = Angular velocity x radius of path

(b) Two forces 30N and 40N act at right angles to each other. Determine by scale drawing, the magnitude and direction of the resultant force, using a scale of 1cm of 5N.

(c) Explain why ships are usually refilled with sand and water after they have been emptied of their cargo.

A floating ship is balanced by its weight and upthrust on it. Hence when offloaded, the upthrust becomes greater than the weight of the ship, therefore, when refilled with sand and water, equilibrium is restored for stability.

(d) A crate of drinks of mass 20kg is placed on a plane inclined at 30° to the horizontal. If the crate slides down with a constant speed,

(i) calculate the coefficient of kinetic friction

$$\scriptsize \mu = tan \theta$$

$$\scriptsize \mu = tan 30$$

$$\scriptsize \mu = 0.5774$$

(ii) calculate the magnitude of the frictional force acting on the crate.
[g = 10ms-2]

Frictional force
f = UR = u x Wcosθ
f = 0.58 x 200 x cos30o
= 0.58 x 200 x 0.8660
= 100N

## Question 9

(a) Define specific latent heat of vaporization.

The specific latent heat of vaporization is the quantity of heat that is required to change the state of a unit mass of a liquid to a gaseous state.

(b) (i) What are renewable energy sources?

Renewable energy sources are the sources where replaceable energy being used up can be gotten or found. They are sources of energy hat cannot be exhausted.

(ii) List four renewable energy sources.

The four sources include: - Sun - Wind - Water - Garbage (Biomass) - Geothermal, etc

(c) Explain why tomatoes keep longer when kept in a moist jute bag in a clay pot.

A moist jute bag in a clay pot is always wet and the temperature is low and cool. The tomatoes kept in this bag are being preserved and with the low temperature, heat loss or gain will be neglected.

(d) (i) A box has a volume of 0.28m3 and is 70% filled with iron fillings at 25oC. Calculate the total mass of the iron fillings

[Density of iron = 8.00 x 103Kgm-3, specific latent heat of fusion of iron = 1.38 x 105JKg-1, specific heat capacity of iron = 460JKg-1K-1, melting point of iron = 1500oC]

Given:
Volume V = 0.28m3

The iron fillings volume = $$\frac{70}{100}\scriptsize \: \times \: 0.28 = 0.196cm^3$$

Total mass, m = ?

Density = $$\frac{mass}{volume}$$

Mass = Density x volume

Mass = 8000 x 0.196 = 1568kg

(ii) Calculate the energy required to melt 10% of the iron fillings.

Energy = ml + mcΔθ

= ml + mc(θ2 - θ1)
= (1568 x 1.38 x 105) + (1568 x 460(1500-25))
= 216384000 + 1.06 x 109
= 1.28 x 109J

## Question 10

(a) (i) What is resonance?

Resonance is the effect felt/observed when a body vibrating with its own natural frequency transfers its frequency to the bodies around it, such that they all vibrate with the same frequency.

(ii) State two examples of resonance.

- Vibrating turning fork
- Soldiers marching on a bridge
- Repeated jumping of a diver at the free end of a diving board causes the board to resonate.
- Rattling of car engine at high speed causing vibrating of the body of the car.

(iii) Differentiate between loudness and intensity of sound

Intensity can be described as the rate of flow of energy per unit time; while loudness is the magnitude of the sensation resulting from a sound reaching the ear.

Loudness depends on the individual hearing ability while intensity depends on physical quantities of energy, time and area.

(b) When a ray is refracted through a rectangular glass prism, which of the following properties of the ray will change?
Wavelength, frequency, and speed.

Wavelength and speed will change and the frequency will remain constant.

(c)

(ii) On the copied diagram, sketch the pattern of the waves immediately after passing through the opening.

(d) (i) A diverging lens of focal length 18.0m is used to view a shark that is 90.0m away from the lens. If the image formed is 1.0m long, calculate the image distance

Given:
Focal length, f = 18m
Objective size, u = 90m
Image size, v =  unknown
Image height, h = 1m

$$\frac{1}{u} \: + \: \frac{1}{v} = \frac{1}{f}$$

$$\frac{1}{v} = \frac{1}{f} \: - \: \frac{1}{v}$$

$$\frac{1}{v} = \frac{1}{-18} \: - \: \frac{1}{90}$$

$$\frac{1}{v} = \frac{-5 - 1}{90}$$

$$\frac{1}{v} = \frac{-6}{90}$$

$$\frac{1}{v} = \frac{-1}{15}$$

v = -15m

The negative value of v indicates that v is a virtual image.

(ii) If the image formed is 1.0m long, calculate the length of the shark.

M = $$\frac{v}{u} = \frac{Image height}{Object height} = \frac{h_i}{h_o}$$

$$\scriptsize h_o = \normalsize \frac{h_i \: \times \: u }{v}$$

$$\scriptsize h_o = \normalsize \frac{1 \: \times \:90 }{15}$$

= 6.0m

## Question 11

(a) (i) Define the coulomb.

Coulomb is the quantity of electricity passing a section of conductor in one second when the current is one ampere.

(ii) Define resistance

Resistance is the driving force that creates opposition to the flow of current in a circuit

(b) State the three effects of an electric current

- Chemical effect
- Magnetic effect
- Heating or thermal effect

(c) (i) State the standard international colour convention for the insulating material covering this electrical wire in a three-pin plug. : (i) live; (ii) neutral; (iii) earth.

(i) Live - Red/Brown

(ii) Neutral - Blue/Black

(iii) Earth - Yellow/Green

(d) (i)

A water melon of mass 5.0kg is suspended on a uniform rod of mass 4.0kg and 4.0m long as illustrated in the diagram above. If the rod is in equilibrium by the action of the force between the charges +q and -q, calculate the anticlockwise moment
[g = 10ms-2]

F  =

Clockwise moment
Cw = 4 x 10 x 1 = 40Nm
Cw = 1.44 x 109q2 x 2 = 2.88 x 109q2Nm

(ii)

A water melon of mass 5.0kg is suspended on a uniform rod of mass 4.0kg and 4.0m long as illustrated in the diagram above. If the rod is in equilibrium by the action of the force between the charges +q and -q, calculate the value of q.
[g = 10ms-²]

Recall that:
Acw = Cw
50 = 40 + 2.88 x 109q2
10 = 2.88 x 109q2
q2 = 10/2.88x109 = 3.47x10-9
q = √ 3.47x10-9 = 5.89x10-5C

## Question 12

(a) Define nucleon number

Nucleon number is the total number of proton of protons and neutrons in an atom of an element

(b) (i) radioactive isotope of Americium (Am - 241) decays into nucleus of Neptunium (Np - 237) and an alpha (α) particle as shown in the nuclear equation below.
24195Am → 237CNp + baα
State the number of neutrons in the nucleus of Americium -241.

Number of neutrons = 241 - 95 = 146

(b) (ii) A radioactive isotope of Americium (Am - 241) decays into nucleus of Neptunium (Np - 237) and an alpha (α) particle as shown in the nuclear equation below.
24195Am → 237CNp + baα
Determine the values of a, b and c.

24195Am → 237cNp + ba

Recall that ba∝ = 42He

24195Am → 2372Np + 42He

a = 2

b = 4

95 = c+2;

c = 93

(c) (i) Why are γ-rays not deflected by electromagnetic fields?

γ-rays have no mass and no charge. Electromagnetic field has no effect on them.

(ii) State two properties of gamma rays that make them suitable for sterilizing medical equipment.

- High penetrating energy that makes it pass through tissues and kill viruses and bacteria
- Ionization energy: They are ionizing radiations.

(d) A sample of radioactive substance was found to be left with 1/32 of its initial count rate after 110 years. Calculate its decay constant.

## Question 1

(a) What is a projectile?

A projectile is an object which can be fashioned to form a parabola. The trajectory of a projectile is usually parabolic or curvilinear.

(b) Give the reason why the horizontal component of the velocity of a projectile remains the same at every point of its flight.

- Zero air resistance
- Zero horizontal forces; hence no acceleration and no change in the velocity

## Question 2

A body is projected at an angle of 30oto the horizontal with a velocity of 150ms-1. Calculate the time it takes the greatest height. [Take g = 10ms-2 and neglect air resistance]

Given:
θ = 30o; u = 150ms-1; t = ? and g = 10ms-2
→ The time taken to reach maximum height, t =?

Recall that

t = $$\frac{usin \theta}{g}$$

t = $$\frac{150 \: \times \: sin 30^o}{10}$$

t = $$\frac{75}{10}$$

= 7.5s

## Question 3

A wire of length 2.00 m and radius 1.0 mm is stretched by 25.0 mm on the application of a force of 103 N. Calculate the Young's modulus for the wire.

Solution

Given:
L = 2m

r = 1mm = 1 x 10-3m

e = 25mm = 25 x 10-3m

F = 100oN

Young modules, E = $$\frac{Fl}{Ae}$$

Area, A = πr2 = 3.142 x (10-3)2 = 3.142 x 10-6

Young modules, E = $$\frac{Fl}{Ae}$$

= $$\frac{1000 \: \times \: 2.00}{3.142 \: \times \: 10^{-6} \: \times \: 25 \: \times \: 10^{-3}}$$

= $$\scriptsize 2.547 \: \times \: 10^{10} NM^{-2}$$

## Question 4

State three ways of increasing the rate of cooling of a cup of hot tea.

- Increasing the surface area by blowing

- Mixing

- Stirring

- Reducing the ambient temperature

## Question 5

(a) What is doping in a semi-conductor?

Doping in a semiconductor is the addition of impurities to a pure semiconductor to increase its electrical conductivity through an increase in the number of holes and electrons or charge carriers.

(b) Draw the symbol for OR gate.

## Question 6

(a) The circuit above consists of an a.c voltage input, a diode, a resistor, and a voltmeter. Identify the circuit.

The circuit is a half-wave rectifier

(b) Draw the waveform for the output voltage.

## Question 7

(a) Write the De Broglie equation.

De Broglie's equation is given as

$$\scriptsize \lambda = \normalsize \frac{h}{p} \\ \scriptsize = \normalsize\frac{h}{mv}$$

h = planck's constant

* It should be noted h = 6.63 x 1034Js
mass of the wave particle = m(in kg)
velocity of wave particle = v(in ms-1)
Momentum of wave particle = P(in kgms-1)

(b) Explain the significance of the equation

The significance of the equation is that it shows that matter has a dual nature, it can exist as a wave and as a particle.

## Question 8

(a) (i) Define uniform acceleration

Uniform acceleration is the acceleration of a body when it is undergoing a constant time rate of change in velocity.

(a) (ii) Write an equation that relates linear velocity, angular velocity and radius of path in circular motion.

V = wr

V = Linear/Tangential velocity
w = Angular velocity

Linear velocity = Angular velocity x radius of path

(b) Two forces 30N and 40N act at right angles to each other. Determine by scale drawing, the magnitude and direction of the resultant force, using a scale of 1cm of 5N.

(c) Explain why ships are usually refilled with sand and water after they have been emptied of their cargo.

A floating ship is balanced by its weight and upthrust on it. Hence when offloaded, the upthrust becomes greater than the weight of the ship, therefore, when refilled with sand and water, equilibrium is restored for stability.

(d) A crate of drinks of mass 20kg is placed on a plane inclined at 30° to the horizontal. If the crate slides down with a constant speed,

(i) calculate the coefficient of kinetic friction

$$\scriptsize \mu = tan \theta$$

$$\scriptsize \mu = tan 30$$

$$\scriptsize \mu = 0.5774$$

(ii) calculate the magnitude of the frictional force acting on the crate.
[g = 10ms-2]

Frictional force
f = UR = u x Wcosθ
f = 0.58 x 200 x cos30o
= 0.58 x 200 x 0.8660
= 100N

## Question 9

(a) Define specific latent heat of vaporization.

The specific latent heat of vaporization is the quantity of heat that is required to change the state of a unit mass of a liquid to a gaseous state.

(b) (i) What are renewable energy sources?

Renewable energy sources are the sources where replaceable energy being used up can be gotten or found. They are sources of energy hat cannot be exhausted.

(ii) List four renewable energy sources.

The four sources include: - Sun - Wind - Water - Garbage (Biomass) - Geothermal, etc

(c) Explain why tomatoes keep longer when kept in a moist jute bag in a clay pot.

A moist jute bag in a clay pot is always wet and the temperature is low and cool. The tomatoes kept in this bag are being preserved and with the low temperature, heat loss or gain will be neglected.

(d) (i) A box has a volume of 0.28m3 and is 70% filled with iron fillings at 25oC. Calculate the total mass of the iron fillings

[Density of iron = 8.00 x 103Kgm-3, specific latent heat of fusion of iron = 1.38 x 105JKg-1, specific heat capacity of iron = 460JKg-1K-1, melting point of iron = 1500oC]

Given:
Volume V = 0.28m3

The iron fillings volume = $$\frac{70}{100}\scriptsize \: \times \: 0.28 = 0.196cm^3$$

Total mass, m = ?

Density = $$\frac{mass}{volume}$$

Mass = Density x volume

Mass = 8000 x 0.196 = 1568kg

(ii) Calculate the energy required to melt 10% of the iron fillings.

Energy = ml + mcΔθ

= ml + mc(θ2 - θ1)
= (1568 x 1.38 x 105) + (1568 x 460(1500-25))
= 216384000 + 1.06 x 109
= 1.28 x 109J

## Question 10

(a) (i) What is resonance?

Resonance is the effect felt/observed when a body vibrating with its own natural frequency transfers its frequency to the bodies around it, such that they all vibrate with the same frequency.

(ii) State two examples of resonance.

- Vibrating turning fork
- Soldiers marching on a bridge
- Repeated jumping of a diver at the free end of a diving board causes the board to resonate.
- Rattling of car engine at high speed causing vibrating of the body of the car.

(iii) Differentiate between loudness and intensity of sound

Intensity can be described as the rate of flow of energy per unit time; while loudness is the magnitude of the sensation resulting from a sound reaching the ear.

Loudness depends on the individual hearing ability while intensity depends on physical quantities of energy, time and area.

(b) When a ray is refracted through a rectangular glass prism, which of the following properties of the ray will change?
Wavelength, frequency, and speed.

Wavelength and speed will change and the frequency will remain constant.

(c)

(ii) On the copied diagram, sketch the pattern of the waves immediately after passing through the opening.

(d) (i) A diverging lens of focal length 18.0m is used to view a shark that is 90.0m away from the lens. If the image formed is 1.0m long, calculate the image distance

Given:
Focal length, f = 18m
Objective size, u = 90m
Image size, v =  unknown
Image height, h = 1m

$$\frac{1}{u} \: + \: \frac{1}{v} = \frac{1}{f}$$

$$\frac{1}{v} = \frac{1}{f} \: - \: \frac{1}{v}$$

$$\frac{1}{v} = \frac{1}{-18} \: - \: \frac{1}{90}$$

$$\frac{1}{v} = \frac{-5 - 1}{90}$$

$$\frac{1}{v} = \frac{-6}{90}$$

$$\frac{1}{v} = \frac{-1}{15}$$

v = -15m

The negative value of v indicates that v is a virtual image.

(ii) If the image formed is 1.0m long, calculate the length of the shark.

M = $$\frac{v}{u} = \frac{Image height}{Object height} = \frac{h_i}{h_o}$$

$$\scriptsize h_o = \normalsize \frac{h_i \: \times \: u }{v}$$

$$\scriptsize h_o = \normalsize \frac{1 \: \times \:90 }{15}$$

= 6.0m

## Question 11

(a) (i) Define the coulomb.

Coulomb is the quantity of electricity passing a section of conductor in one second when the current is one ampere.

(ii) Define resistance

Resistance is the driving force that creates opposition to the flow of current in a circuit

(b) State the three effects of an electric current

- Chemical effect
- Magnetic effect
- Heating or thermal effect

(c) (i) State the standard international colour convention for the insulating material covering this electrical wire in a three-pin plug. : (i) live; (ii) neutral; (iii) earth.

(i) Live - Red/Brown

(ii) Neutral - Blue/Black

(iii) Earth - Yellow/Green

(d) (i)

A water melon of mass 5.0kg is suspended on a uniform rod of mass 4.0kg and 4.0m long as illustrated in the diagram above. If the rod is in equilibrium by the action of the force between the charges +q and -q, calculate the anticlockwise moment
[g = 10ms-2]

F  =

Clockwise moment
Cw = 4 x 10 x 1 = 40Nm
Cw = 1.44 x 109q2 x 2 = 2.88 x 109q2Nm

(ii)

A water melon of mass 5.0kg is suspended on a uniform rod of mass 4.0kg and 4.0m long as illustrated in the diagram above. If the rod is in equilibrium by the action of the force between the charges +q and -q, calculate the value of q.
[g = 10ms-²]

Recall that:
Acw = Cw
50 = 40 + 2.88 x 109q2
10 = 2.88 x 109q2
q2 = 10/2.88x109 = 3.47x10-9
q = √ 3.47x10-9 = 5.89x10-5C

## Question 12

(a) Define nucleon number

Nucleon number is the total number of proton of protons and neutrons in an atom of an element

(b) (i) radioactive isotope of Americium (Am - 241) decays into nucleus of Neptunium (Np - 237) and an alpha (α) particle as shown in the nuclear equation below.
24195Am → 237CNp + baα
State the number of neutrons in the nucleus of Americium -241.

Number of neutrons = 241 - 95 = 146

(b) (ii) A radioactive isotope of Americium (Am - 241) decays into nucleus of Neptunium (Np - 237) and an alpha (α) particle as shown in the nuclear equation below.
24195Am → 237CNp + baα
Determine the values of a, b and c.

24195Am → 237cNp + ba

Recall that ba∝ = 42He

24195Am → 2372Np + 42He

a = 2

b = 4

95 = c+2;

c = 93

(c) (i) Why are γ-rays not deflected by electromagnetic fields?

γ-rays have no mass and no charge. Electromagnetic field has no effect on them.

(ii) State two properties of gamma rays that make them suitable for sterilizing medical equipment.