- This paper consists of sections A and B with a total of ten (10) questions.
- Answer all questions from section A and two (2) questions from section B.
- Marks for each questions or part thereof are indicated.
- Mathematical tables and non-programmable calculators may be used.
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
- Pie, \( \pi = 3.14 \)
- Molar gas constant, \( R_0 = 8.31 \, \text{l/molK} \)
- Radius of the sun, \( R_s = 7.04 \times 10^8 \, \text{m} \)
- Stefan's constant, \( \delta = 5.72 \times 10^{-8} \, \text{W/m}^2 \, \text{K}^4 \)
- Electronic charge, \( e = 1.6 \times 10^{-19} \, \text{C} \)
- Boltzman constant, \( k = 1.38 \times 10^{-23} \, \text{J/K} \)
Answer all questions in this section
State the principle of homogeneity of dimension and hence state on what principle is it based on?
The equation of a wave is given by \( y = r \sin \left[ \omega \left( \frac{x}{v} - k\pi \right) \right] \) where all the symbols carry their usual meaning. What are dimensions and units of "x" and "k"?
Differentiate between mistake and an error? Give one example for each
A form five student performs an experiment to determine the young's modulus of a wire exactly 2m long, by Searle's method. In a particular reading the student measures the extension in the length of the wire to be 0.8mm with an error of \(\pm 0.05mm\) at a load of exactly 2.5kg. The student also measures the diameter of the wire as 0.38mm with an error of \(\pm 0.02mm\). Find the error for the calculated value of the young modulus from this information.
State Newton's second and third laws of motion.
A body is allowed to slide down from the top of a smooth inclined plane of inclination of 45\(^\circ\) with horizontal. Another identical body is allowed to fall vertically from the top point of the same plane, what is the ratio of the times taken by the first body to the second body to reach the ground?
A block of mass 12.5kg lying on a rough horizontal surface is acted upon by a horizontal force of 45N and another force 30N at angle of 30\(^\circ\) to the vertical as indicated by figure 1 below. Find the coefficient of friction between the block and surface in order to be in equilibrium.
Write two applications of projectile motion.
Two tall buildings are 200m apart. With what speed must a ball be thrown horizontally from a window of one building 1.5km above the ground so that it will enter a window 450m from the ground in the other?
Give one common difference between physical pendulum and simple pendulum.
A metal rod of length 20cm suspended from a fixed point tied at its centre by a steel wire. When the wire is twisted the rod oscillates with a period of 2sec. Two discs of mass 5g each are attached at each end of the rod, and new period is found to be 2.5sec. Find the moment of inertia of the rod.
The total energy of an atom oscillating in a crystal lattice at temperature "T" is on average 3KT, assuming that copper atoms each of mass \(1.06 \times 10^{-25} kg\), execute S.H.M of amplitude \(8 \times 10^{-11} m\) 300K. Calculate the corresponding frequency.
State Newton's law of universal gravitation.
The figure below shows three masses in space. What are the magnitude and the direction of the net gravitational force on the 5.0kg mass?
20 Cm
20 Kg
10 Cm
10 kg
Sketch and explain the graph showing the variation of gravitation potential with the distance from the surface of a planet both inside and outside.
A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape the solar system?
The resistance thermometer and gas thermometers may show different values in measuring the temperature of the surrounding. Explain the reason behind.
Sketch the graph to show the three phases of water at triple point.
State equipartition theorem.
Estimate the mass of an ash particle used in Brownian motion experiment which is moving with root mean square velocity of \(1 \times 10^{-2} m/s\) at room temperature of \(27^\circ C\).
A cylinder contains 3.00mol of helium gas at temperature of \(27^0 C\).
(i) If the gas is heated at constant volume, how much energy must be transferred by heat to the gas for its temperature to increase to \(227^0 C\)? (02marks)
(ii) How much energy must be transferred by heat to the gas at constant pressure to raise the temperature to \(227^0 C\)? (02marks)
State laws of black body radiation.
The temperature of a furnace is \(2324^0 C\) and the intensity in its radiation spectrum is maximum nearly at 1200Ã…. Calculate the surface temperature of the star that emits radiation of wavelength of nearly 4800Ã….
A roof measures \(20m \times 50m\) and is blackened. If the temperature of the sun's surface is 6000K and the distance of the sun from the earth is \(1.5 \times 10^{11} m\). Calculate how much solar energy is incident on the roof per minute, assuming that half is lost in passing through the earth's atmosphere, the roof being normal to the sun's rays.
Briefly explain the following terms:
(i) Volcano. (01mark)
(ii) Volcanic eruption. (01mark)
Briefly explain how do Primary waves differ from Secondary waves? Give three (3) points.
The seismometer at town A recorded the time interval of 10seconds between the Arrivals of Primary waves and Secondary waves due to an earth quake that occurred in may 2002. Locate the focus of the earth quake if the Secondary waves travel at about \(4km/s\) and the Primary waves at \(8km/s\).
Explain three (3) effects of global warming.
Answer two (2) questions from this section
Upon which principle Kirchhoff's current law (junction rule) is based?
What is the advantage of measuring unknown resistance with a wheat stone bridge? (Give three (3) points)
The light dependent resistor (LDR) in the circuit below is found to have resistance 800Ω in moon light and resistance 160Ω in a light. Calculate the voltmeter reading, \(V_m\), in moon light with switch S open. (02marks)
If the reading of the voltmeter in day light with the switch S closed is also equal to \( V_m \), what is the value of the resistance R? (03marks)
A 60V, 10W lamp is to be run on 100V, 60Hz a. c, mains
(i) Calculate the inductance of a choke coil required. (03marks)
(ii) If resistance is used instead of choke, what will be its value? (03marks)
Briefly explain about Depletion layer and Reverse leakage current as used in Pn-junction.
Explain why addition of small quantity of suitable impurities to an intrinsic semiconductor decreases its resistivity.
The mobility "\(\mu\)" of charge carriers in a conductor is defined by equation \( V = \mu E \). Where "V" represents drift velocity produced by an electric field "E". A rod of P - type germanium of length 10mm and cross-sectional area \( 1mm^2 \) contains \( 3.0 \times 10^{21} \) holes i.e the number of electrons density is negligible. Given that the mobility of holes is \( 0.35m^2v^{-1}S^{-1} \), what is the resistance between the ends of the rod?
Identify two types of bipolar transistors.
Which among the transistor mentioned in c(i) above responds quickly to electrical signal? Give reason.
Determine the Q - point of the transistor circuit shown in the figure below. Also draw the d.c load line. Given that \(\beta = 200\) and \( V_{BE} = 0.7V \).
Vcc = 20V
Give three (3) main differences between practical Op-amp and an ideal Op-amp.
The figure below shows the multi-stage Op-amp circuit, the resistor values are \(R_f = 470k\Omega, R_1 = 4.3k\Omega, R_2 = R_3 = 33k\Omega\). Find the output voltage for an input of 80\(\mu V\).
State two (2) conditions for the summing up amplifier to act as averaging amplifier.
Draw the circuit representing Op-amp as voltage follower and give two features of it.
Define the term modulation as used in telecommunication.
A 2500kHz carrier is modulated by audio signal with frequency span of 50-15000Hz. What are the frequencies of lower and upper side bands? What is the bandwidth required to handle the output?
Instructions
- This paper consists of sections A and B with a total of ten (10) questions.
- Answer all questions from section A and two (2) questions from section B.
- Marks for each questions or part thereof are indicated.
- Mathematical tables and non-programmable calculators may be used.
Useful Information
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
- Pie, \( \pi = 3.14 \)
- Molar gas constant, \( R_0 = 8.31 \, \text{J/molK} \)
- Radius of the sun, \( R_s = 7.04 \times 10^8 \, \text{m} \)
- Stefan's constant, \( \sigma = 5.72 \times 10^{-8} \, \text{W/m}^2 \, \text{K}^4 \)
- Electronic charge, \( e = 1.6 \times 10^{-19} \, \text{C} \)
- Boltzmann constant, \( k = 1.38 \times 10^{-23} \, \text{J/K} \)
SECTION A (70 Marks)
Answer all questions in this section
State the principle of homogeneity of dimension and hence state on what principle is it based on?
Answer:
The principle of homogeneity of dimensions states that for an equation to be dimensionally correct, the dimensions of all terms on both sides of the equation must be identical. This means that we can only add, subtract, or compare quantities that have the same dimensions.
This principle is based on the fundamental principle of dimensional analysis, which states that physical laws are independent of the units used to measure the physical quantities.
The equation of a wave is given by \( y = r \sin \left[ \omega \left( \frac{x}{v} - k\pi \right) \right] \) where all the symbols carry their usual meaning. What are dimensions and units of "x" and "k"?
Answer:
In the wave equation \( y = r \sin \left[ \omega \left( \frac{x}{v} - k\pi \right) \right] \):
For x (position/distance):
- Dimension: [L] (Length)
- Units: meter (m)
For k (wave number):
- Dimension: [L⁻¹] (Reciprocal length)
- Units: per meter (m⁻¹)
Explanation: The argument of a sine function must be dimensionless. Since ωt has dimension [T⁻¹][T] = dimensionless, and x/v has dimension [L][T/L] = [T], we need k to have dimension [L⁻¹] to make kÏ€ dimensionless when multiplied by x (which has dimension [L]).
Differentiate between mistake and an error? Give one example for each.
Answer:
Mistake: A mistake is a blunder or incorrect action due to carelessness or misunderstanding. It can be avoided by being careful and attentive.
Example: Reading a scale incorrectly (e.g., reading 5.2 cm as 5.7 cm).
Error: An error is the difference between the measured value and the true value of a quantity. Errors are inherent in the measurement process and cannot be completely eliminated.
Example: Parallax error when reading a measuring scale from an angle rather than perpendicularly.
A form five student performs an experiment to determine the Young's modulus of a wire exactly 2m long, by Searle's method. In a particular reading the student measures the extension in the length of the wire to be 0.8mm with an error of \(\pm 0.05mm\) at a load of exactly 2.5kg. The student also measures the diameter of the wire as 0.38mm with an error of \(\pm 0.02mm\). Find the error for the calculated value of the Young modulus from this information.
Answer:
The formula for Young's modulus is:
Where:
F = mg = 2.5 × 9.8 = 24.5 N (no error in mass or g)
L = 2 m (no error in length)
ΔL = 0.8 mm = 0.0008 m, error = ±0.05 mm = ±0.00005 m
d = 0.38 mm = 0.00038 m, error = ±0.02 mm = ±0.00002 m
The fractional error in Y is given by:
Since F and L have no errors:
Substituting values:
Therefore, the percentage error in Y is:
The error in the calculated value of Young's modulus is approximately 16.77%.
State Newton's second and third laws of motion.
Answer:
Newton's Second Law: The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.
Mathematically: \( F = ma \), where F is the net force, m is mass, and a is acceleration.
Newton's Third Law: For every action, there is an equal and opposite reaction. When one body exerts a force on another, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
A body is allowed to slide down from the top of a smooth inclined plane of inclination of 45° with horizontal. Another identical body is allowed to fall vertically from the top point of the same plane, what is the ratio of the times taken by the first body to the second body to reach the ground?
Answer:
Let the height of the inclined plane be h, and its length be L.
For the body falling vertically:
For the body sliding down the inclined plane:
Acceleration along the plane: \( a = g\sin\theta = g\sin45° = \frac{g}{\sqrt{2}} \)
Distance to travel: \( L = \frac{h}{\sin45°} = h\sqrt{2} \)
Ratio of times:
The ratio of the time taken by the first body (on inclined plane) to the second body (falling vertically) is √2 : 1.
A block of mass 12.5kg lying on a rough horizontal surface is acted upon by a horizontal force of 45N and another force 30N at angle of 30° to the vertical as indicated by figure 1 below. Find the coefficient of friction between the block and surface in order to be in equilibrium.
Answer:
Resolving forces:
Vertical components:
Horizontal components:
For equilibrium, F = μR
The coefficient of friction is approximately 0.404.
Write two applications of projectile motion.
Answer:
- Military applications: Calculating trajectories of missiles, bullets, and artillery shells.
- Sports: Analyzing the motion of balls in games like basketball, football, and cricket.
- Space exploration: Planning satellite launches and calculating orbital trajectories.
Two tall buildings are 200m apart. With what speed must a ball be thrown horizontally from a window of one building 1.5km above the ground so that it will enter a window 450m from the ground in the other?
Answer:
Vertical distance fallen: h = 1500 - 450 = 1050 m
Time to fall this distance:
Horizontal distance to cover: 200 m
The ball must be thrown with a horizontal speed of approximately 13.66 m/s.
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