MITIHANI POPOTE RXAMINATION SERIES.
FOR FORM ADVANCES SECONDARY SCHOOLS
PRE-NATIONAL EXAMINATION SERIES
PHYSICS 1 - SERIES 4
131/01
TIME: 2:30 HRS
NOVEMBER, 2025
Instructions
- This paper consists of section A and B with total of ten (10) questions.
- Answer all questions in section A and any two (2) questions from section B.
- Mathematical tables and non-programmable calculator may be used.
- Cellular phones and unauthorized materials are not allowed in the examination room.
- Write your examination number on every page of your answer booklet(s).
The following information may be useful:
- Acceleration due to gravity \( g = 9.8m/s^2 \)
- Radius of the earth \( R_e = 6400km \)
- Mass of an electron \( m_e = 9.1 \times 10^{-31}kg \)
- Universal molar gas constant \( R = 8.31/mol^{-1}K^{-1} \)
- \( 1eV = 1.6 \times 10^{-19}C \)
- \( 1mmHg = 133.3224Pa \)
- \( Pie \pi = 3.14 \)
- Density of water \( \rho_w = 1000kg/m^3 \)
SECTION A (70 marks)
Answer all questions from this section.
1. (10 marks)
(a) (i) Explain two categories of physical quantities (02 marks)
(ii) The frequency "n" of vibration of stretched string is a function of its tension F the length "/" and the mass per unit length "m" using the knowledge of dimension- to write the expression of "n" (2.5 marks)
(b) Explain three (3) causes of random errors. (1.5 marks)
(c) In an experiment to determine the value of young's modulus of elasticity of steel, a wire of length 325cm (measured by a metre scale of least count 0.1cm) is loaded by a mass of 2kg and it is found that it stretches by 0.227cm (measured by a micrometer having least count 0.001cm). The diameter if the wire as measured by a screw gauge (least count = 0.001cm) is found to be 0.043cm. Calculate the maximum permissible error. (04 marks)
2. (10 marks)
(a) (i) State the principle of conservation of linear momentum (02 marks)
(ii) A ball of mass 0.1kg moving horizontally at a speed of 5m/s collides head on with a ball of 0.3kg at rest. Assuming that the collision is perfectly elastic, determine the final velocities of the two balls. (03 marks)
(b) (i) Is there any point on the projectile path at which the acceleration is perpendicular to the velocity? (02 marks)
(ii) A boy throws a ball horizontally with velocity of of 8m/s from the top of a building. The ball falls to the ground 12m away from the building. What is the height of the building? (03 marks)
3. (10 marks)
(a) Differentiate gravitational field from gravitational field strength. (02 marks)
(b) (i) At what height from the surface of earth will the value of "g" be reduced by 36% from the value at the surface? (2.5 marks)
(ii) What is the acceleration due to gravity on a surface of a planet that has a radius one third that of the earth and the same average density? (2.5 marks)
(c) Give reasons for the following statements.
(i) The outer rail of a curved railway track generally is raised over the inner. (01 mark)
(ii) A pilot does not fall when his caroplane loops a vertical loop. (01 mark)
(iii) A horse has to apply more force to start a cart than to keep it moving. (01 mark)
4. (10 marks)
(a) (i) Give four (4) examples of simple harmonic motion (02 marks)
(ii) Calculate the period for a particle executing simple harmonic motion with acceleration of 16cm/s² at a distance of 4cm from the equilibrium position. (02 marks)
(b) A tray of mass 12kg is supported by two identical springs as shown in the figure below. When the tray is displaced slightly and released it executes S.H.M with a period of 1.5 seconds.
(i) What is the force constant is each spring? (01 mark)
(ii) When a block of mass "m" is placed above the tray, the period of oscillation changes to 3.0seconds what is the value of "m" (03 marks)
(c) State four (4) applications of rotational motion of rigid bodies. (02 marks)
5. (10 marks)
(a) (i) State the conditions for establishment of temperature scale. (02 marks)
(ii) A liquid – in glass thermometer uses a liquid volume which varies with temperature according to the equation \( V_\theta = V_0 \left(1 + a\theta + b\theta^2\right) \) Where \( V_\theta \) and \( V_0 \) are the volumes of the gas at \( \theta^\circ C \) and \( 0^\circ C \) respectively, and "a" and "b" are constants. If \( a = b \times 10^3 \), what will be the reading of the liquid in glass scale when the actual temperature is \( 60^\circ C \) (03 marks)
(b) (i) What do you understand by the term composite conductors. (01 mark)
(ii) Two perfectly lagged bars "x" and "y" are arranged in series and parallel. When the bars are in series the hot end of "x" is maintained at \( 90^\circ C \) and the cold end of "y" is maintained at \( 30^\circ C \), when the bars are in parallel the hot end of each is maintained at \( 90^\circ C \) and the cold end is maintained at \( 30^\circ C \). Calculate the ration of the total rate of flow of heat in parallel arrangement to that in series arrangement. The length of each bar is L and cross-section area A (thermal conductivity of X is \( 400 \, \text{w} \, m^{-1} \, k^{-4} \) and that of y is \( 200 \, \text{w} \, m^{-1} \, k^{-4} \)) (04 marks)
6. (10 marks)
(a) Highlight the differences between isothermal and adiabatic process. (at least six (6) points) (03 marks)
(b) An ideal gas at \( 17^\circ C \) has a pressure of \( 760 \, \text{mmHg} \) and is compressed.
(i) Isothermally
(ii) Adiabatically.
Until its volume is halved. Calculate in each case the final pressure and temperature of gas. (\( y = 1.4 \)) (04 marks)
(c) One mole of an ideal gas which is kept at temperature of \( 320 \, \text{k} \) is compressed isothermally from its initial volume of 8 litres to a final volume of 4 litres; calculate the total work done in the whole process. (03 marks)
7. (10 marks)
(a) (i) Define the term drift velocity (0.5 marks)
(ii) Find the total momentum (p) acquired by the electrons in a wire of length 35cm when a current of 2.5A starts to flow. (1.5 marks)
(b) (i) Mention two (2) advantages of wheat stone bridge.
(ii) In a meter bridge shown in the figure below, the null point is found at a distance of 40cm from A. If a resistance of 15Ω is connected in parallel with \( R_2 \) and null point occurs at 53cm, determine the values of \( R_1 \) and \( R_2 \). (03 marks)
(c) (i) What is the resonant frequency of RLC circuit with resistance 5Ω, inductance 3mH and capacitance 1μF? (01 mark)
(ii) If an a.c source of constant voltage amplitude 4V is set to this frequency, what is the average power transferred to the circuit? (02 marks)
(iii) Determine the Q factor of this circuit. (01 mark)
(iv) Determine the band width of this circuit. (01 mark)
SECTION B (30 marks)
Answer any two (2) questions from this section.
8. (15 marks)
(a) (i) Explain the concept of virtual earth. (01 mark)
(ii) Derive an expression for the gain of non-inverting amplifier. (02 marks)
(b) Using the circuit shown in the figure below and given
\[ V_{1} = 0.45V, \, V_{2} = 1.5V \, and \, R_{1} = R_{2} = R_{3} = R_{4} = 95k\Omega. \]
(i) Write down the relationship between output voltage "V" and input voltages \( V_{1} \, and \, V_{2} \). (03 marks)
(ii) What will be the value of the output voltage? (04 marks)
(c) Discuss the advantage of digital over analogue modes of presenting information. (03 marks)
A transmitter radiates a total power of 10kW. Its carrier is modulated to a depth of 60% Calculate.
(i) The power of the carrier. (02 marks)
(ii) The power in each side band. (02 marks)
9. (15 marks)
(a) State and explain the energy bands in solids. What are the essential features of the energy bands in solids? (04 marks)
(b) (i) Discuss the factors that contribute to the decrease in efficiency of the transistor, explain how to overcome those factors.
(ii) Draw a circuit diagram of npm transistor with its emitter- base junction at forward bias and base- collector junction at reverse bias. (02 marks)
(c) The figure below shows a circuit for a junction transistor voltage amplifier.
(i) What is the function of capacitors \( C_1 \) and \( C_2 \) and resistor \( R_1 \) and \( R_L \) (02 marks)
(ii) Derive expressions for the voltage gain and power gain. (02 marks)
(iii) Given the supply voltage,
\[V_{CE} = 10V, \, V_{CE} = 0.31V\]
Collector current \( I_c \) is 3nA. Assume that the base emitter voltage \( V_{BE} \) is 0.7V and the current gain \( \beta \) is 100. Calculate the values of resistor \( R_L \) and \( R_1 \) (05 marks)
10. (15 marks)
(a) (i) Discuss the green house effect and its importance in daily life experience in plant growth (04 marks)
(ii) What is meant by soil permeability and soil porosity (03 marks)
(b) (i) What do you understand by the term solar photo voltaics. (01 mark)
(ii) A solar cell of surface area \( 100cm^2 \) is illuminated by a monochromatic light of a wavelength of 760nm and power density of \( 1000mw^{-2} \) the open circuit voltage is 0.67V when the cell temperature is 300K. Calculate the dark cell current \( I_o \) assuming 100% quantum efficiency. (07 marks)
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Instructions
- This paper consists of section A and B with total of ten (10) questions.
- Answer all questions in section A and any two (2) questions from section B.
- Mathematical tables and non-programmable calculator may be used.
- Cellular phones and unauthorized materials are not allowed in the examination room.
- Write your examination number on every page of your answer booklet(s).
The following information may be useful:
- Acceleration due to gravity \( g = 9.8m/s^2 \)
- Radius of the earth \( R_e = 6400km \)
- Mass of an electron \( m_e = 9.1 \times 10^{-31}kg \)
- Universal molar gas constant \( R = 8.31J/mol^{-1}K^{-1} \)
- \( 1eV = 1.6 \times 10^{-19}J \)
- \( 1mmHg = 133.3224Pa \)
- \( \pi = 3.14 \)
- Density of water \( \rho_w = 1000kg/m^3 \)
(a) (i) Explain two categories of physical quantities (02 marks)
Fundamental quantities: Basic quantities that cannot be defined in terms of other physical quantities (e.g., mass, length, time, electric current, temperature, amount of substance, luminous intensity).
Derived quantities: Quantities derived from fundamental quantities through mathematical operations (e.g., velocity, acceleration, force, energy, pressure).
(ii) The frequency "n" of vibration of stretched string is a function of its tension F, the length "l" and the mass per unit length "m". Using dimensional analysis, write the expression of "n" (2.5 marks)
Let n = k Fa lb mc
Dimensions: [T⁻¹] = [MLT⁻²]a [L]b [ML⁻¹]c
Equating dimensions:
For M: 0 = a + c
For L: 0 = a + b - c
For T: -1 = -2a
Solving: a = 1/2, c = -1/2, b = -1
Therefore: n = k√(F/(ml))
(b) Explain three (3) causes of random errors. (1.5 marks)
1. Parallax error: Incorrect reading due to viewing measurement from an angle rather than directly perpendicular.
2. Environmental fluctuations: Variations in temperature, pressure, or humidity during measurements.
3. Instrument limitations: Finite resolution of measuring instruments leading to estimation errors.
(c) In an experiment to determine the value of Young's modulus of elasticity of steel, a wire of length 325cm (measured by a metre scale of least count 0.1cm) is loaded by a mass of 2kg and it is found that it stretches by 0.227cm (measured by a micrometer having least count 0.001cm). The diameter of the wire as measured by a screw gauge (least count = 0.001cm) is found to be 0.043cm. Calculate the maximum permissible error. (04 marks)
Young's modulus Y = (FL)/(AΔL) = (4FL)/(πd²ΔL)
Relative error: ΔY/Y = ΔF/F + ΔL/L + 2Δd/d + Δ(ΔL)/ΔL
ΔF = 0 (mass is exact), ΔL = 0.1cm, Δd = 0.001cm, Δ(ΔL) = 0.001cm
ΔY/Y = 0 + (0.1/325) + 2(0.001/0.043) + (0.001/0.227)
ΔY/Y = 0.000308 + 0.0465 + 0.00441 = 0.05122 ≈ 5.12%
Maximum permissible error = 5.12%
(a) (i) State the principle of conservation of linear momentum (02 marks)
The total linear momentum of an isolated system remains constant if no external forces act on the system.
(ii) A ball of mass 0.1kg moving horizontally at a speed of 5m/s collides head on with a ball of 0.3kg at rest. Assuming that the collision is perfectly elastic, determine the final velocities of the two balls. (03 marks)
Using conservation of momentum and kinetic energy:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
0.1×5 + 0.3×0 = 0.1v₁ + 0.3v₂
0.5 = 0.1v₁ + 0.3v₂ ...(1)
For elastic collision: v₁ - v₂ = -(u₁ - u₂)
v₁ - v₂ = -(5 - 0) = -5 ...(2)
Solving equations (1) and (2):
v₁ = -2.5 m/s, v₂ = 2.5 m/s
The 0.1kg ball rebounds at 2.5 m/s, and the 0.3kg ball moves forward at 2.5 m/s.
(b) (i) Is there any point on the projectile path at which the acceleration is perpendicular to the velocity? (02 marks)
Yes, at the maximum height of the projectile path, the acceleration (vertically downward due to gravity) is perpendicular to the velocity (which is purely horizontal at that point).
(ii) A boy throws a ball horizontally with velocity of 8m/s from the top of a building. The ball falls to the ground 12m away from the building. What is the height of the building? (03 marks)
Horizontal motion: x = vₓt ⇒ 12 = 8t ⇒ t = 1.5s
Vertical motion: y = ½gt² = ½ × 9.8 × (1.5)² = 4.9 × 2.25 = 11.025m
Height of the building = 11.03m
(a) Differentiate gravitational field from gravitational field strength. (02 marks)
Gravitational field: A region of space around a mass where another mass experiences a force of attraction.
Gravitational field strength: The force per unit mass experienced by a small test mass placed in the field. g = F/m (unit: N/kg or m/s²)
(b) (i) At what height from the surface of earth will the value of "g" be reduced by 36% from the value at the surface? (2.5 marks)
g' = g(R/(R+h))² = 0.64g (since reduced by 36%)
(R/(R+h))² = 0.64
R/(R+h) = 0.8
R+h = R/0.8 = 1.25R
h = 0.25R = 0.25 × 6400 = 1600km
(ii) What is the acceleration due to gravity on a surface of a planet that has a radius one third that of the earth and the same average density? (2.5 marks)
g = GM/R² = G(ρ×4/3πR³)/R² = (4/3)πGρR
Since density ρ is same, g ∝ R
Rplanet = Rearth/3
gplanet = gearth/3 = 9.8/3 = 3.27 m/s²
(c) Give reasons for the following statements:
(i) The outer rail of a curved railway track generally is raised over the inner. (01 mark)
To provide the necessary centripetal force for trains moving along the curve, reducing wear on rails and increasing safety.
(ii) A pilot does not fall when his aeroplane loops a vertical loop. (01 mark)
At the top of the loop, the normal reaction and pilot's weight both act downward, providing the required centripetal force.
(iii) A horse has to apply more force to start a cart than to keep it moving. (01 mark)
Static friction is greater than kinetic friction, so more force is needed to overcome static friction and start motion.
Note: Answers for Section B questions would follow the same format as Section A.
Contact with MITIHANI POPOTE:
WhatsApp: +255 716 655 236
WhatsApp Channel: https://whatsapp.com/channel/0029VbA7XZkBvvsZxay5kl1l
Web: https://mitihanipopote.blogspot.com/
Instagram: https://www.instagram.com/higher_awaits
Facebook: https://www.facebook.com/profile.php?id=100064001654581
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