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Quiz 2 of 14

# 2020 Physics WAEC Theory Past Questions

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## Question 1

An elastic material of length 3m is to be stretched to produce an extension three times its original length. Calculate the force required to produce the extension if the force constant of the material is 982.3Nm-1

Solution

F = Ke

K = 982.3

e = 3 x 3

F = Ke

= 982.3 x 3 x 3

= 8840.7N

## Question 2

In a solar panel for heat supply, state the function of each of the following parts:

(a) Metal flat plate

(b) Thermal insulator

To minimize heat loss

(c) Tubes

To help circulate heat

## Question 3

(a) In the design of an optical, what type of material is most suitable for the design of the core?

(a) Material most suitable for the design of core of an optical fiber:

i. Glass or plastics

(b) State one condition necessary to confine signals to the core of an optical fibre.

The refractive index must be greater than that of the cladding.

## Question 4

The velocity v of a wave in a stretched string depends on the tension, T, in the spring and the mass per unit length of μ of the spring. Obtain an expression for v in terms of T and μ, using the method of dimensions.

Solution

$$\scriptsize V \propto T^a \mu^b$$

$$\scriptsize V = KT^a \mu^b$$

K is dimensionless

$$\scriptsize [V] = K[T] ^a[\mu]^b$$

$$\scriptsize LT^{-1} = K(MLT^{-2})^a(ML^{-1})^b$$

$$\scriptsize LT^{-1} = KM^{a+b}L^{a-b}T^{-2ab}$$

For T = -2a

a = $$\frac{1}{2}$$

V = $$\scriptsize KT^{-\frac{1}{2}}$$

= $$\scriptsize KT^{-\frac{1}{2}} \mu^{-\frac{1}{2}}$$

V = $$\scriptsize K\sqrt{\frac{T}{\mu}}$$

## Question 5

A satellite launched with velocity VE just escapes the earth's gravitational attraction. given that the radius of the earth is R, show that VE$$\scriptsize \sqrt{20}R$$[g=10ms-2]

Solution

To show that VE$$\scriptsize \sqrt{20}R$$

K.E = Gravtational potential energy

$$\normalsize\frac{1}{2} \scriptsize mv^2_ E = \normalsize \frac{GmM}{R}$$

$$\scriptsize v^2_ E = \normalsize \frac{2GmM}{Rm}$$

$$\scriptsize v^2_ E = \normalsize \frac{2G\not{m}M}{R\not{m}}$$

$$\scriptsize v^2_ E = \normalsize \frac{2GM}{R}$$

GM = gR2

$$\scriptsize v^2_ E = \normalsize \frac{2GR^2}{R}$$

$$\scriptsize v^2_ E = 2gR$$

$$\scriptsize v_ E = \sqrt{2gR}$$

g = 10ms-2

$$\scriptsize v_ E = \sqrt{2 \: \times\: 10R}$$

$$\scriptsize v_ E = \sqrt{20R}$$

## Question 6

A bullet is fired from a gun at 300 to the horizontal. The bullet remains in flight for 25s before touching the ground. Calculate the velocity of the projection. [g=10ms-2].

Solution

Time of flight = $$\frac{2usin \theta}{g}$$

25 = $$\frac{2usin 30}{10}$$

2u = $$\frac{25 \: \times \: 30}{sin 30}$$

u = 250ms-1

## Question 7

State three properties of lasers that make them preferable to ordinary light beam.

Solution

Properties of laser beams are:

-Travels a long distance without losing its intensity

-has a narrow optical bandwidth

-emitted continuously

-gives more intense power

-they are coherent

-monochromatic

## Question 8

a) (i) Define a torque.

Torque turning effect of force about an axis/pivot. It is defined as the product of force and the perpendicular distance between the force acting point and the pivot point.

(ii) State three factors that determine a torque.

i. Perpendicular distance from the pivot

ii. Direction of the force

iii. Magnitude of the force

(b) (i) Define free fall.

Freefall is the vertical motion of a body under gravity or its own weight

(ii) A body is thrown vertically upwards from the top of a tower 40.0m high with a velocity of 10.0ms-1. Calculate the time taken for the body to reach the ground. [g=10ms-2]

Solution

H = $$\scriptsize ut \pm \normalsize \frac{1}{2} \scriptsize gt^2$$

40 = $$\scriptsize 10t \pm \normalsize \frac{1}{2} \scriptsize \: \times \: 10 \: \times \: t^2$$

(t + 2)(t - 4) = 0

Time to fall to the ground, t = 4s

(c) A cube of wood of side 8.0cm, floats at the interface between oil and water 2.0cm of its lower surface below the interface as shown in the diagram below. Given that the relative densities of oil and water are 0.72 and 1.00 respectively, calculate the mass of the wood.

Solution

Mass of wood = upthrust to the water displaced x upthrust due to oil displaced.

= (1000 x 2 x 8 x 8 x 10-6) + (720 x 6 x 8 x 8 x10-6)

=0.404kg

## Question 9

(a) (i) Explain resonance frequency as applied in RLC series circuit.

It is the frequency of oscillation of an RLC series circuit when the capacitance reactance is equal to the inductive reactance

i.e. Xc = XL

The impedance is equal to the resistance. When current is maximum, impedance is minimum.

(ii) Sketch a diagram to illustrate the vibration of frequency, f, with the resistance, R, the capacitive reactance, Xc, and the inductive reactance, XL, in RLC series circuit.

(iii) Using the diagram drawn in 9(a)(ii), state whether the current in the circuit leads, lags or is in phase with the supply volatge when: ($$\scriptsize \propto$$ ) f = f0; ($$\scriptsize \gamma$$ ) f>f0 Where f0 is the resonance frequency.

Relationship between I and V when f = fo, current is in phase with supply voltage.

• Current lags behind voltage

F<fo

• Current leads the voltage when

F >FO

(b) (i) Define mutual inductance

Mutual Inductance is the ratio of the induced e.m.f in one coil to the time rate change of  current in the other coil.

(ii) The coil of an electric generator has 500 turns and 8.0cm diameter. If it rotates in a magnetic field of density 0.25T, calculate the angular speed when its peak voltage is 480V. [  π =3.142]

Angular speed of the coil in electric generator.

E = WBAN

480 = $$\scriptsize w \: \times \: 0.25 \: \times \: \pi \left(\normalsize \frac{8.0 \: \times \: 10^{-12}}{2} \right)\: \times \: 500$$

(c) (i) Explain eddy currents.

Eddy current: This is the current-induced flows within a metal block when there is a magnetic flux linking the circuit.

OR

Loops of electric current induced within a conductor by changing magnetic flux field in the conductor.

(ii) State two practical uses of eddy currents.

i. Induction coil

ii. Induction furnace

iii. Speedometer

iv. Induction motors

## Question 10

(a) (i) Define critical angle as used in optics.

Critical angle: This is the angle of incidence in the optically denser medium for which the angle of refraction in the less dense medium is 90º

(ii) State two conditions necessary for total internal reflection to occur

- Light must travel from a dense medium to a less dense medium

- Angle of incidence in the denser medium must be greater than the critical angle.

(iii)  List three practical applications of total internal reflection.

Practical applications are:

• Prism binoculars
• Prism telescope
• Fisheye wide view
• Fiber optics

(b) State two effects of refraction.

Effects of refraction include

• Mirages
• Dispersion of white light
• Straight objects appear bent at the interface of the media
• Rainbow
• The real and apparent depth

(c) (i) Define progressive waves.

A disturbance traveling through a medium that enables energy to be transferred from its source to another without the movement of the particles of the medium is called progressive wave.

It can also be defined as wave which travels continuously in a medium in the same direction without the change in its amplitude.

(ii) A plane progressive wave is represented by the equation y = $$\scriptsize 0.5sin \left(100 \pi t \: -\: \normalsize \frac{100 \pi}{17} \right)$$

Where y is in millimetres, t in second, and x in metres. Calculate the:

(a) frequency of the wave;

Solution

y = $$\scriptsize Asin \left(2 \pi ft \: -\: \normalsize \frac{2 \pi}{\lambda} \right)$$

2πf = 1000π

F = $$\frac{1000}{2}$$

= 500Hz

(b) wavelength of the wave;

Solution

$$\frac{2 \pi x}{\lambda} = \frac{100 \pi x}{17}$$

$$\scriptsize \lambda = \normalsize \frac{2 \: \times \: 17}{100}$$

= 0.34m

(c) speed of the wave;

Solution

V = $$\scriptsize f \lambda$$

V = $$\scriptsize 500 \: \times \: 0.34$$

= 170ms-1

## Question 11

(a) In an experiment to measure the specific latent heat of vapourization of water, a student places a heater in a beaker containing water. The beaker stands on an electronic balance so that the mass of the beaker is switched on and readings taken every 100s when the water starts boiling.

The table below shows the readings.

 Time/s 0 100 200 300 400 Reading on balance/g 203.22 201.62 199.79 198.26 196.50 Mass of water evaporated 0 Energy supplied by heater/J 0

(i) Fill in the mass of water evaporated.

(ii) Given that the heater supplies energy at the rate of 38J/s, fill in the 100s, 200s, 300s, and 400s.

(iii) Plot a graph of energy supplied on the vertical axis and mass of water evaporated on the horizontal axis, starting both axes from the origin (0,0).

(iv) Determine the slope of the graph.

Solution

S = $$\frac{\Delta Q}{\Delta m}$$

S = $$\frac{12.0 \: \times \: 10^3}{5.3}$$

= $$\scriptsize 2.26 \: \times \: 10^3 J/g$$

(v) What does the value of the slope mean?

2.26 x 103j heat energy is needed to evaporate 1g of water at constant temperature.

(b) (i) Explain what is meant by saturated vapour pressure

(i) At any given temperature, some molecules of a liquid in a given system escape from the liquid surface as a vapour

-Vapour pressure is built up above the liquid surfaces

-When the rate of escape is equal to the rate at which they return to the liquid

(ii) State the factor that affects saturated vapour pressure

Temperature

## Question 12

(i) Define isotopes.

(a) (i) Isotopes are atoms that have the same atomic number but different mass number

(ii) Mention two uses of radioactive tracers in each of the following areas:

(1) medicine

• Monitoring function of thyroid gland or other organs
• Detection of blood clots in the brain
• Diagnosis and treatment of diseases.
• Sterilization of equipments

(2) industry

• Detection of leakages in pipes underground.
• Detection of wearing and tearing of moving parts

(3) agriculture

• Study of photosynthesis mechanism
• Sterilization of insects
• Food preservation

(b) When light of frequency 5.4 x 1014Hz is incident on a metal surface, the maximum energy of the emitted electrons is 1.2x10-19J. Calculate the minimum frequency of radiation for which electrons can be emitted. [h=6.6x10-34Js].

Solution

E = h (f - fo)

fo = $$\scriptsize f \: - \: \normalsize \frac{E}{h}$$

= $$\scriptsize 5.4 \: \times \: 10^{14} \: - \: \normalsize \frac{1.2 \: \times \: 10^{-14}}{6.6 \: \times \: 10^{-34}}$$

= 3.6 x 1014Hz

(c) State three features common to electromagnetic waves.

• Travels with speed of light
• Undergoes refraction, reflection, diffraction, polarization/interference
• Travels through the vacuum

(d) (i) Mention four components of the nuclear reactor.

(ii) State the function of each of the components stated in 12(d)(i)

• Uranium (fuel)
• Boron – Graphite moderator(control) neutron population/fission
• Coolant- reduces excessive heat generates during reaction.
• Heat exchanger – converts heat energy to other forms.
• Shield- to protectrotect the operators from radiation.

## Question 1

An elastic material of length 3m is to be stretched to produce an extension three times its original length. Calculate the force required to produce the extension if the force constant of the material is 982.3Nm-1

Solution

F = Ke

K = 982.3

e = 3 x 3

F = Ke

= 982.3 x 3 x 3

= 8840.7N

## Question 2

In a solar panel for heat supply, state the function of each of the following parts:

(a) Metal flat plate

(b) Thermal insulator

To minimize heat loss

(c) Tubes

To help circulate heat

## Question 3

(a) In the design of an optical, what type of material is most suitable for the design of the core?

(a) Material most suitable for the design of core of an optical fiber:

i. Glass or plastics

(b) State one condition necessary to confine signals to the core of an optical fibre.

The refractive index must be greater than that of the cladding.

## Question 4

The velocity v of a wave in a stretched string depends on the tension, T, in the spring and the mass per unit length of μ of the spring. Obtain an expression for v in terms of T and μ, using the method of dimensions.

Solution

$$\scriptsize V \propto T^a \mu^b$$

$$\scriptsize V = KT^a \mu^b$$

K is dimensionless

$$\scriptsize [V] = K[T] ^a[\mu]^b$$

$$\scriptsize LT^{-1} = K(MLT^{-2})^a(ML^{-1})^b$$

$$\scriptsize LT^{-1} = KM^{a+b}L^{a-b}T^{-2ab}$$

For T = -2a

a = $$\frac{1}{2}$$

V = $$\scriptsize KT^{-\frac{1}{2}}$$

= $$\scriptsize KT^{-\frac{1}{2}} \mu^{-\frac{1}{2}}$$

V = $$\scriptsize K\sqrt{\frac{T}{\mu}}$$

## Question 5

A satellite launched with velocity VE just escapes the earth's gravitational attraction. given that the radius of the earth is R, show that VE$$\scriptsize \sqrt{20}R$$[g=10ms-2]

Solution

To show that VE$$\scriptsize \sqrt{20}R$$

K.E = Gravtational potential energy

$$\normalsize\frac{1}{2} \scriptsize mv^2_ E = \normalsize \frac{GmM}{R}$$

$$\scriptsize v^2_ E = \normalsize \frac{2GmM}{Rm}$$

$$\scriptsize v^2_ E = \normalsize \frac{2G\not{m}M}{R\not{m}}$$

$$\scriptsize v^2_ E = \normalsize \frac{2GM}{R}$$

GM = gR2

$$\scriptsize v^2_ E = \normalsize \frac{2GR^2}{R}$$

$$\scriptsize v^2_ E = 2gR$$

$$\scriptsize v_ E = \sqrt{2gR}$$

g = 10ms-2

$$\scriptsize v_ E = \sqrt{2 \: \times\: 10R}$$

$$\scriptsize v_ E = \sqrt{20R}$$

## Question 6

A bullet is fired from a gun at 300 to the horizontal. The bullet remains in flight for 25s before touching the ground. Calculate the velocity of the projection. [g=10ms-2].

Solution

Time of flight = $$\frac{2usin \theta}{g}$$

25 = $$\frac{2usin 30}{10}$$

2u = $$\frac{25 \: \times \: 30}{sin 30}$$

u = 250ms-1

## Question 7

State three properties of lasers that make them preferable to ordinary light beam.

Solution

Properties of laser beams are:

-Travels a long distance without losing its intensity

-has a narrow optical bandwidth

-emitted continuously

-gives more intense power

-they are coherent

-monochromatic

## Question 8

a) (i) Define a torque.

Torque turning effect of force about an axis/pivot. It is defined as the product of force and the perpendicular distance between the force acting point and the pivot point.

(ii) State three factors that determine a torque.

i. Perpendicular distance from the pivot

ii. Direction of the force

iii. Magnitude of the force

(b) (i) Define free fall.

Freefall is the vertical motion of a body under gravity or its own weight

(ii) A body is thrown vertically upwards from the top of a tower 40.0m high with a velocity of 10.0ms-1. Calculate the time taken for the body to reach the ground. [g=10ms-2]

Solution

H = $$\scriptsize ut \pm \normalsize \frac{1}{2} \scriptsize gt^2$$

40 = $$\scriptsize 10t \pm \normalsize \frac{1}{2} \scriptsize \: \times \: 10 \: \times \: t^2$$

(t + 2)(t - 4) = 0

Time to fall to the ground, t = 4s

(c) A cube of wood of side 8.0cm, floats at the interface between oil and water 2.0cm of its lower surface below the interface as shown in the diagram below. Given that the relative densities of oil and water are 0.72 and 1.00 respectively, calculate the mass of the wood.

Solution

Mass of wood = upthrust to the water displaced x upthrust due to oil displaced.

= (1000 x 2 x 8 x 8 x 10-6) + (720 x 6 x 8 x 8 x10-6)

=0.404kg

## Question 9

(a) (i) Explain resonance frequency as applied in RLC series circuit.

It is the frequency of oscillation of an RLC series circuit when the capacitance reactance is equal to the inductive reactance

i.e. Xc = XL

The impedance is equal to the resistance. When current is maximum, impedance is minimum.

(ii) Sketch a diagram to illustrate the vibration of frequency, f, with the resistance, R, the capacitive reactance, Xc, and the inductive reactance, XL, in RLC series circuit.

(iii) Using the diagram drawn in 9(a)(ii), state whether the current in the circuit leads, lags or is in phase with the supply volatge when: ($$\scriptsize \propto$$ ) f = f0; ($$\scriptsize \gamma$$ ) f>f0 Where f0 is the resonance frequency.

Relationship between I and V when f = fo, current is in phase with supply voltage.

• Current lags behind voltage

F<fo

• Current leads the voltage when

F >FO

(b) (i) Define mutual inductance

Mutual Inductance is the ratio of the induced e.m.f in one coil to the time rate change of  current in the other coil.

(ii) The coil of an electric generator has 500 turns and 8.0cm diameter. If it rotates in a magnetic field of density 0.25T, calculate the angular speed when its peak voltage is 480V. [  π =3.142]

Angular speed of the coil in electric generator.

E = WBAN

480 = $$\scriptsize w \: \times \: 0.25 \: \times \: \pi \left(\normalsize \frac{8.0 \: \times \: 10^{-12}}{2} \right)\: \times \: 500$$

(c) (i) Explain eddy currents.

Eddy current: This is the current-induced flows within a metal block when there is a magnetic flux linking the circuit.

OR

Loops of electric current induced within a conductor by changing magnetic flux field in the conductor.

(ii) State two practical uses of eddy currents.

i. Induction coil

ii. Induction furnace

iii. Speedometer

iv. Induction motors

## Question 10

(a) (i) Define critical angle as used in optics.

Critical angle: This is the angle of incidence in the optically denser medium for which the angle of refraction in the less dense medium is 90º

(ii) State two conditions necessary for total internal reflection to occur

- Light must travel from a dense medium to a less dense medium

- Angle of incidence in the denser medium must be greater than the critical angle.

(iii)  List three practical applications of total internal reflection.

Practical applications are:

• Prism binoculars
• Prism telescope
• Fisheye wide view
• Fiber optics

(b) State two effects of refraction.

Effects of refraction include

• Mirages
• Dispersion of white light
• Straight objects appear bent at the interface of the media
• Rainbow
• The real and apparent depth

(c) (i) Define progressive waves.

A disturbance traveling through a medium that enables energy to be transferred from its source to another without the movement of the particles of the medium is called progressive wave.

It can also be defined as wave which travels continuously in a medium in the same direction without the change in its amplitude.

(ii) A plane progressive wave is represented by the equation y = $$\scriptsize 0.5sin \left(100 \pi t \: -\: \normalsize \frac{100 \pi}{17} \right)$$

Where y is in millimetres, t in second, and x in metres. Calculate the:

(a) frequency of the wave;

Solution

y = $$\scriptsize Asin \left(2 \pi ft \: -\: \normalsize \frac{2 \pi}{\lambda} \right)$$

2πf = 1000π

F = $$\frac{1000}{2}$$

= 500Hz

(b) wavelength of the wave;

Solution

$$\frac{2 \pi x}{\lambda} = \frac{100 \pi x}{17}$$

$$\scriptsize \lambda = \normalsize \frac{2 \: \times \: 17}{100}$$

= 0.34m

(c) speed of the wave;

Solution

V = $$\scriptsize f \lambda$$

V = $$\scriptsize 500 \: \times \: 0.34$$

= 170ms-1

## Question 11

(a) In an experiment to measure the specific latent heat of vapourization of water, a student places a heater in a beaker containing water. The beaker stands on an electronic balance so that the mass of the beaker is switched on and readings taken every 100s when the water starts boiling.

The table below shows the readings.

 Time/s 0 100 200 300 400 Reading on balance/g 203.22 201.62 199.79 198.26 196.50 Mass of water evaporated 0 Energy supplied by heater/J 0

(i) Fill in the mass of water evaporated.

(ii) Given that the heater supplies energy at the rate of 38J/s, fill in the 100s, 200s, 300s, and 400s.

(iii) Plot a graph of energy supplied on the vertical axis and mass of water evaporated on the horizontal axis, starting both axes from the origin (0,0).

(iv) Determine the slope of the graph.

Solution

S = $$\frac{\Delta Q}{\Delta m}$$

S = $$\frac{12.0 \: \times \: 10^3}{5.3}$$

= $$\scriptsize 2.26 \: \times \: 10^3 J/g$$

(v) What does the value of the slope mean?

2.26 x 103j heat energy is needed to evaporate 1g of water at constant temperature.

(b) (i) Explain what is meant by saturated vapour pressure

(i) At any given temperature, some molecules of a liquid in a given system escape from the liquid surface as a vapour

-Vapour pressure is built up above the liquid surfaces

-When the rate of escape is equal to the rate at which they return to the liquid

(ii) State the factor that affects saturated vapour pressure

Temperature

## Question 12

(i) Define isotopes.

(a) (i) Isotopes are atoms that have the same atomic number but different mass number

(ii) Mention two uses of radioactive tracers in each of the following areas:

(1) medicine

• Monitoring function of thyroid gland or other organs
• Detection of blood clots in the brain
• Diagnosis and treatment of diseases.
• Sterilization of equipments

(2) industry

• Detection of leakages in pipes underground.
• Detection of wearing and tearing of moving parts

(3) agriculture

• Study of photosynthesis mechanism
• Sterilization of insects
• Food preservation

(b) When light of frequency 5.4 x 1014Hz is incident on a metal surface, the maximum energy of the emitted electrons is 1.2x10-19J. Calculate the minimum frequency of radiation for which electrons can be emitted. [h=6.6x10-34Js].

Solution

E = h (f - fo)

fo = $$\scriptsize f \: - \: \normalsize \frac{E}{h}$$

= $$\scriptsize 5.4 \: \times \: 10^{14} \: - \: \normalsize \frac{1.2 \: \times \: 10^{-14}}{6.6 \: \times \: 10^{-34}}$$

= 3.6 x 1014Hz

(c) State three features common to electromagnetic waves.

• Travels with speed of light
• Undergoes refraction, reflection, diffraction, polarization/interference
• Travels through the vacuum

(d) (i) Mention four components of the nuclear reactor.

(ii) State the function of each of the components stated in 12(d)(i)