WAEC SSCE - Physics - 2021

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As the metallic sphere is heated, the temperature increases, causing the metal atoms to vibrate more rapidly. This increased vibration causes an increase in the space between the atoms, resulting in an increase in volume. Since the mass of the sphere remains constant, the increase in volume results in a decrease in density. Therefore, the correct option is: "Its volume increases and its density decreases".

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To measure the potential difference across a resistor using a galvanometer, the student needs a high value resistor connected in series with the galvanometer. The high value resistor acts as a voltage divider, allowing the galvanometer to measure the potential difference without being damaged by excessive current. This is known as a voltmeter circuit, and it is commonly used in electronics to measure voltage. A low value resistor connected in parallel with the galvanometer would be used to measure current, not voltage.

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The statement that best describes the particles in a solid at room temperature is "close together and vibrating". In a solid, the particles are tightly packed and held together by strong forces of attraction, so they cannot move freely. However, they do have some kinetic energy, causing them to vibrate around their fixed positions. This means that the particles do not move randomly like in a gas, but rather they maintain their positions while vibrating.

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The opening in the eye through which light passes to the retina is called the "pupil". The pupil is a small, round hole located in the center of the iris (the colored part of the eye), which regulates the amount of light that enters the eye. The size of the pupil can change depending on the amount of light available and the focus required for near or far vision. The light that enters the eye through the pupil is then focused by the cornea and lens onto the retina at the back of the eye, which sends visual information to the brain through the optic nerve.

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To calculate the energy required to raise the temperature of an ice cube from 5°C to 0°C, we need to use the specific heat capacity of ice, which is 2.1 J/g°C. The formula for calculating the energy required to change the temperature of a substance is: Energy = mass x specific heat capacity x change in temperature We are given that the mass of the ice cube is 20 g, and we want to raise its temperature by 5°C (from 5°C to 0°C). Plugging in the values into the formula, we get: Energy = 20 g x 2.1 J/g°C x 5°C Simplifying the equation, we get: Energy = 210 J Therefore, the energy required to raise the temperature of the ice cube from 5°C to 0°C is 210 J. The correct option is 4) 210 J.

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When gas molecules are compressed at constant temperature, the space they occupy decreases, resulting in more molecules per unit volume. As a result, the molecules make more impact per second on the walls of the container, causing an increase in pressure. Therefore, the correct option is: "The molecules make more impact per second on the walls of the container."

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The scientist who suggested that moving particles exhibit wave properties was Louis de Broglie. De Broglie was a French physicist who developed the theory of wave-particle duality. In his theory, de Broglie proposed that all particles, not just light, have wave-like properties, and that their wavelength is directly proportional to their momentum. This idea challenged the prevailing view of the time, which held that particles and waves were distinct entities, and helped to lay the foundation for the development of quantum mechanics. So, Louis de Broglie is the scientist who suggested that moving particles exhibit wave properties.

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The reason for laminating the soft iron core of a transformer is to reduce eddy currents. Eddy currents are circulating currents that flow in the core of the transformer, and they generate heat and waste energy. By laminating the core into thin sheets, the eddy currents are reduced, which helps to increase the efficiency of the transformer. In other words, laminating the core helps to prevent energy loss and make the transformer run more efficiently.

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To solve this problem, we can use the work-energy theorem, which states that the net work done on an object is equal to its change in kinetic energy. Mathematically, we can express this as: Net work = Change in kinetic energy In this problem, the force is acting continuously, which means that it is doing work on the object. The work done by a constant force can be calculated using the formula: Work = Force x Distance x cos(theta) where theta is the angle between the force vector and the displacement vector. Since the force is in the same direction as the displacement (i.e., they are both acting to the right), we can simplify the formula to: Work = Force x Distance Substituting the given values into this formula, we get: Work = 10 N x Distance Now, we can use the work-energy theorem to find the distance moved by the object. We know that the net work done on the object is equal to its change in kinetic energy, which is: Net work = 60 J - 20 J = 40 J Setting this equal to the work formula above, we get: 10 N x Distance = 40 J Solving for distance, we get: Distance = 4 meters Therefore, the distance moved by the object is 4 meters.

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Pascal's principle states that the pressure applied to a fluid in a closed container will be transmitted equally to all parts of the fluid and to the walls of the container. This means that the pressure in a fluid is transmitted equally in all directions, regardless of the density of the fluid. Therefore, the correct option is "transmitted equally in all directions".

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The power of a person is defined as the amount of work done per unit time. In this case, the work done by the man is equal to his weight multiplied by the height he climbs. Therefore, the work done by the man is: Work = Force x Distance Work = 200 N x 9 m Work = 1800 J The time taken by the man to climb the stairs is 5 seconds. Therefore, the power of the man is: Power = Work / Time Power = 1800 J / 5 s Power = 360 W So the power of the man is 360 watts (W). This means that the man can perform work at a rate of 360 joules per second, which is a measure of his physical exertion during the climb.

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When an electric current flows through a wire, the wire heats up due to the resistance it offers to the flow of electrons. This heat can be dissipated to the surroundings by conduction, convection, and radiation. The amount of heat generated in the wire depends on the resistance of the wire, the current flowing through it, and the time it takes to flow. To minimize the heat generated in the wire, we need to reduce its resistance. The resistance of a wire depends on its length, cross-sectional area, and the resistivity of the material. Among the options given, the most effective way to minimize the heat generated in the wire is to increase the diameter of the wire. This is because the resistance of a wire is inversely proportional to its cross-sectional area. Therefore, a wire with a greater diameter will have less resistance and hence generate less heat than a wire with a smaller diameter. Thicker insulation will not help much in reducing the heat generated in the wire because insulation is used to prevent the electric current from flowing out of the wire, and it does not affect the flow of current in the wire itself. Thinner insulation or smaller diameter wire may even increase the heat generated because it will lead to a higher resistance and hence more heat generation. Therefore, the correct answer is "greater diameter" because it will reduce the resistance of the wire and hence minimize the heat generated in it.

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Electric motor primarily converts electrical energy to mechanical energy. An electric motor is a device that converts electrical energy into mechanical energy by using the magnetic effect of current. When an electric current flows through a coil in a magnetic field, a force is exerted on the coil which causes it to rotate, thus converting electrical energy into mechanical energy.

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The factor that does not affect the rate of evaporation of a liquid is the volume of the liquid. Evaporation is the process of a liquid turning into a gas or vapor, and it occurs when the molecules of the liquid gain enough energy to break away from the surface and enter the surrounding air. The rate of evaporation is affected by several factors, including temperature, wind, and surface area. Temperature is the most important factor that affects the rate of evaporation. As the temperature of the liquid increases, the molecules of the liquid gain more energy and move faster, increasing the chances of the molecules escaping the surface and entering the air. Wind can also affect the rate of evaporation. When there is wind, it removes the humid air around the liquid and replaces it with drier air. This leads to a faster rate of evaporation, as there is more room in the air for the liquid molecules to enter. Surface area is another factor that affects the rate of evaporation. The larger the surface area of the liquid, the more molecules are exposed to the air, leading to a faster rate of evaporation. However, the volume of the liquid does not affect the rate of evaporation. A larger volume of liquid will take longer to evaporate than a smaller volume, but the rate of evaporation is not affected by the volume of the liquid.

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The correct option is: "It has dimension M\(^{-1}\)L\(^{3}\)T\(^{-2}\)." The universal gravitational constant, G, is a fundamental constant in physics that determines the strength of the gravitational force between two objects. Its value is approximately 6.674 × 10\(^{-11}\) N m\(^{2}\)kg\(^{-2}\). The dimension of G is M\(^{-1}\)L\(^{3}\)T\(^{-2}\), which means it has one unit of mass, negative one unit of length cubed, and two units of time in its dimensional formula. Its SI unit is N m\(^{2}\)kg\(^{-2}\). It is a scalar quantity, not a vector quantity, because it only has a magnitude and no direction.

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A heat sensitive resistor made of a semiconductor is called a thermistor. A thermistor is a type of resistor whose resistance changes in response to changes in temperature. They are used in a variety of applications, such as temperature sensing and control, temperature compensation, and over-temperature protection. They work by exploiting the property of certain materials to change their electrical resistance in response to changes in temperature. When the temperature of a thermistor increases, its resistance decreases, and when the temperature decreases, its resistance increases. This relationship can be used to measure temperature with high accuracy.

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To solve this problem, we need to use the formula for electrical energy: Energy = Power x Time where Power = Voltage x Current, and Time is in hours. First, we need to find the power of the bulb. Power = Voltage x Current = 440V x 2.0A = 880W. Since we want to find the cost of keeping the bulb on for two days, which is 48 hours, we can now find the energy used by the bulb: Energy = Power x Time = 880W x 48 hours = 42,240 Wh To convert watt-hours (Wh) to kilowatt-hours (kWh), we need to divide by 1000: 42,240 Wh ÷ 1000 = 42.24 kWh Finally, to find the cost of using 42.24 kWh at a rate of $0.40 per kWh, we multiply the two values: 42.24 kWh x $0.40/kWh = $16.90 Therefore, the answer is $16.90.

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When an atom emits an alpha particle, it may become a different element. An alpha particle is a helium nucleus consisting of two protons and two neutrons. When an atom emits an alpha particle, it loses these two protons and two neutrons and therefore changes its atomic number and becomes a different element. The new element will have an atomic number that is two less than the original element. For example, if an atom of uranium-238 emits an alpha particle, it will become an atom of thorium-234. So, the correct statement is that an atom that emits an alpha particle may become a different element.

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The inductive reactance (X_L) in a circuit can be calculated using the formula X_L = 2πfL, where f is the frequency of the circuit and L is the inductance of the inductor. Given that X_L = 1Ω and f = 100Hz, we can use this formula to calculate the inductance L: X_L = 2πfL 1Ω = 2π * 100Hz * L L = 1Ω / (2π * 100Hz) L = 1.59 x 10^-3H So, the inductance of the inductor is 1.59 x 10^-3 H.

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The electrons in a cathode-ray tube are produced by heating a metal filament. This process is called thermionic emission, which means that when a metal filament is heated, the electrons gain enough energy to escape from the surface of the metal and become free electrons. These free electrons are then accelerated towards the anode (positively charged plate) by applying an electric field to the x-plates, and they pass through a small hole in the anode, creating a narrow beam of electrons. This beam of electrons then passes through the tube and is focused by magnetic fields to produce an image on a fluorescent screen.

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When a ball is swung in a horizontal circle with a constant speed, it experiences a centripetal acceleration directed towards the center of the circle. The centripetal acceleration is the acceleration required to keep an object moving in a circular path, and it is given by the formula: a = v\(^{2}\) / r where v is the speed of the ball and r is the radius of the circle. In this case, the ball is moving in a horizontal circle, so the centripetal acceleration acts vertically towards the center of the circle (O). So, the acceleration of the ball is toward the center O.

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The resistance of a wire can be calculated using the formula: R = ρ * L / A where R is the resistance of the wire, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire. Given the resistivity of the wire (1.1 x 10\(^-{8}\) Ω m) and its resistance (21 Ω), we can calculate the length of the wire as follows: L = R * A / ρ = 21 Ω * (2 * π * 10\(^-{8}\) m\(^{2}\)) / (1.1 x 10\(^-{8}\) Ω m) = 2 * π * 21 / 1.1 = 120 m So, the length of the wire is 120 m.

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The capacitance of a parallel plate capacitor is defined as the ratio of the charge stored on the plates to the potential difference between the plates. Mathematically, we can express this as: C = Q/V where C is capacitance, Q is charge, and V is potential difference. Now, let's consider each of the options in turn and determine how they affect the capacitance of a parallel plate capacitor. I. Decreasing the distance between the plates When the distance between the plates is decreased, the electric field between the plates increases. This, in turn, increases the charge that can be stored on the plates for a given potential difference. As a result, the capacitance of the capacitor increases. II. Increasing the distance between the plates When the distance between the plates is increased, the electric field between the plates decreases. This, in turn, decreases the charge that can be stored on the plates for a given potential difference. As a result, the capacitance of the capacitor decreases. III. Increasing the area of the plates overlap When the area of the plates overlap is increased, the capacitance of the capacitor increases. This is because there is more surface area for the charges to accumulate on, which increases the amount of charge that can be stored on the plates for a given potential difference. IV. Avoiding the use of dielectric between the plates A dielectric is an insulating material that is placed between the plates of a capacitor to increase its capacitance. Without a dielectric, the capacitance of the capacitor will be smaller. Based on the above analysis, we can see that options I and III will increase the capacitance of a parallel plate capacitor. Option II will decrease capacitance and option IV will not have any effect on capacitance. Therefore, the correct answer is: I and III only.

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Resistance is a measure of how much a material opposes the flow of an electric current. The resistance of a wire is influenced by four factors: length, cross-sectional area, material, and temperature. The length of the wire is directly proportional to its resistance, meaning that the longer the wire, the greater its resistance. The cross-sectional area of the wire is inversely proportional to its resistance, meaning that the larger the cross-sectional area, the lower the resistance. The material of the wire affects its resistance, with some materials having higher resistances than others. Finally, temperature affects the resistance of a wire, with most materials having a positive temperature coefficient of resistance, meaning that their resistance increases with temperature. Mass, on the other hand, is not a factor that determines the resistance of a wire. The mass of the wire is related to its density and volume, but it does not affect the flow of current through the wire or its resistance. Therefore, the correct answer is "mass."

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If the relative humidity of the atmosphere increases, the rate of evaporation of sweat from the human body decreases. This is because when the relative humidity is high, the air is already saturated with water vapor, and there is less capacity for more water to evaporate into the air. When sweat evaporates, it cools the skin and removes heat from the body. But if the air is already saturated with water vapor, sweat cannot evaporate as effectively, and the body will have a harder time cooling down. Therefore, high humidity can make it feel hotter and more uncomfortable because the body's natural cooling mechanism is less effective.

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To find the components of Q + R, we need to add the corresponding components of the two vectors. Given the components of Q and R, we have: Q = (-3.0, 5.5) R = (9.2, 4.4) Adding the corresponding components of Q and R, we get: Q + R = (-3.0 + 9.2, 5.5 + 4.4) = (6.2, 9.9) Therefore, the components of Q + R are (6.2, 9.9). To summarize, we can find the components of the sum of two vectors by adding the corresponding components of the two vectors. In this case, the components of Q + R are (6.2, 9.9).

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When the air jet is directed onto the holes in the rotating disc, it causes the air to vibrate at a certain frequency, producing a sound wave. The frequency of the sound wave is determined by the number of holes on the disc and the speed of rotation of the disc. In this case, the note produced has a frequency of 480 Hz and there are 20 holes on the disc. This means that as each hole passes the air jet, it produces a sound wave of 480 Hz. Since there are 20 holes, the disc must rotate 20 times to produce 20 sound waves, which is equivalent to one cycle of the note. Therefore, the speed of rotation of the disc can be calculated by multiplying the frequency of the note by the number of holes and dividing by the number of cycles per second. In this case, we have: Speed of rotation = (480 Hz x 20 holes) / 1 cycle per second Speed of rotation = 9,600 revolutions per second However, the answer choices are given in revolutions per second (rev/s), so we need to convert the speed of rotation to rev/s by dividing by the number of holes: Speed of rotation = 9,600 / 20 Speed of rotation = 480 rev/s Therefore, the correct answer is 24 rev/s.

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Out of the given options, mass is not an example of force. Mass is a measure of the amount of matter in an object and is typically measured in kilograms (kg). Force, on the other hand, is a quantity that describes the interaction between two objects and can cause a change in motion or deformation of an object. Tension, weight, and friction are all examples of forces. Tension is the force transmitted through a string, cable, or rope when it is pulled tight. Weight is the force exerted by gravity on an object with mass, and it is measured in Newtons (N). Friction is the force that opposes motion between two surfaces that are in contact with each other. To summarize, mass is not a force, whereas tension, weight, and friction are all examples of forces.

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The acceleration of a moving object can be determined from the slope of its velocity-time graph. This is because acceleration is defined as the rate of change of velocity over time. Therefore, the steeper the slope of the velocity-time graph, the greater the rate of change of velocity, and thus the greater the acceleration. On the other hand, the distance-time graph only provides information about the distance covered by an object over time, and the area under this graph only gives the total distance traveled. The velocity-time graph, however, shows how the velocity of the object changes over time, and the slope of this graph gives information about the acceleration. Therefore, the slope of the velocity-time graph is a more direct and reliable way to determine the acceleration of a moving object.

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The set of quantities that have members which are all vectors is "Force, displacement and momentum." A vector is a quantity that has both magnitude and direction. Force, displacement, and momentum all have both magnitude and direction, making them vector quantities. Pressure, energy, distance, acceleration, work, density, volume, and weight are not all vectors because they do not have both magnitude and direction.

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The correct option is: "exhibit vibratory motion." The molecules of solids and liquids are constantly in motion, but the type of motion they exhibit differs. In solids, the molecules are packed closely together and vibrate in place. The vibrations are not enough to overcome the attractive forces between the molecules, so the molecules are held in a fixed position. In liquids, the molecules are not as closely packed together as in solids, and they have more freedom of movement. The molecules are in constant motion, but they are still attracted to each other, so they tend to stay close together. The motion of the molecules in liquids is more rapid and random than in solids, but they still exhibit a vibratory motion. Therefore, the statement "They both exhibit vibratory motion" is the correct statement about the molecules of solids and liquids.

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The work done in stretching the elastic material can be determined by finding the area under the curve of the load-extension graph. Unfortunately, for a complex shaped curve like the one in this graph, determining the area requires calculus or a planimeter which is a mechanical instrument for measuring the area of an enclosed figure.

However, we can estimate the work done by dividing the graph into simpler shapes for which we can calculate the area. Since the graph looks like a right triangle followed by a curve, we can estimate the area by summing the area of the triangle and a rectangular area that approximates the curved part.

Here's a step-by-step approach to estimate the work done:

1. Identify the relevant data: From the graph, identify the following:
   • The extension on the x-axis (represented by the label "Extension/cm") at the point where the curve departs from the straight line. Let's call this extension value Xd.
   • The load on the y-axis (represented by the label "Load/N") at the point where the curve departs from the straight line. Let's call this load value Yd.
2. Calculate the area of the triangle: The triangle represents the work done within the elastic limit of the material. Since it's a right triangle, its area is calculated as 0.5 * base * height. In this case, the base of the triangle is Xd (extension) and the height is Yd (load).
3. Estimate the area under the curve: The curved part of the graph represents the additional work done beyond the elastic limit. Since we cannot determine the exact area under the curve, we can estimate it by drawing a rectangle that fits under the curve as much as possible. The base of this rectangle will be the same as the base of the triangle (Xd) and the height will be the difference between the maximum load (Ymax) on the y-axis and Yd (the load at the elastic limit).
4. Sum the areas: The total estimated work done is the sum of the area of the triangle and the area of the rectangle.

Determination of work done from the graph: Work done is the area under the graph

Area = 12 $\frac{1}{2}$ b * h = 12×10−2×4 $\frac{1}{2}\times {10}^{-2}\times 4$ = 2×10−2 $2\times {10}^{-2}$J

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(a) Two artificial satellites are the International Space Station (ISS) and the Hubble Space Telescope.

(b) To calculate the speed of a geostationary satellite, you can use the formula:
Speed = √(GM/r)
Where G is the gravitational constant (6.67 x 10^-11 m^3/kg s^2), M is the mass of the Earth (5.97 x 10^24 kg), and r is the radius of the orbit (6300 km or 6.3 x 10^6 m).
Plugging in the numbers, we get:
Speed = √(6.67 x 10^-11 x 5.97 x 10^24 / 6.3 x 10^6) Speed = √(40,000) m/s Speed = 200 m/s
So the geostationary satellite moves at a speed of about 200 meters per second in its orbit.
Note that this is just an approximation, and the actual speed can vary slightly due to factors such as the shape of the Earth and the satellite's altitude.

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Wave-particle duality is a concept in physics that describes the behavior of light and other subatomic particles as both a wave and a particle. This means that light can exhibit properties of both waves (such as diffraction and interference) and particles (such as quantization and the photoelectric effect).

To calculate the value of Planck's constant, h, we can use the equation relating the momentum of a particle, p, and its wavelength, λ:

p = h / λ

where h is Planck's constant.

Given the values of the momentum (1.6 x 10^-23 kg m/s) and wavelength (4.2 x 10^-11 m) of the particle, we can calculate h by rearranging the equation:

h = p * λ

h = (1.6 x 10^-23 kg m/s) * (4.2 x 10^-11 m)

h = 6.72 x 10^-34 Js

So, the value of Planck's constant, h, is 6.72 x 10^-34 Js.

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(a): Analyzing the Circuit

(i) Setting Up the Circuit:

Refer to the diagram provided to ensure you connect the battery, ammeter, voltmeter, resistance box, key, and connecting wires correctly. Here's a general guideline:

1. Follow the standard circuit diagram for this experiment.
2. Connect the components in series. Pay attention to polarities: positive to positive and negative to negative for the battery and voltmeter.
3. The ammeter needs to be inserted in the loop where you want to measure current.
4. The resistance box is placed in series with the other components.
5. The key acts as a switch to control the current flow.

(ii) Measuring EMF with Key Open

• With the key in the open position (circuit off), the voltmeter will measure the electromotive force (EMF) of the battery, denoted by E₀. Record this value.

(iii) Measuring Current and Calculating Reciprocal with Key Closed

• Close the key (circuit on).
• Select a resistance value (R) on the resistance box, for example, 1 Ω.
• Use the ammeter to measure the current (I) flowing through the circuit. Record this value.
• Calculate the reciprocal of the current (1/I).

(iv) Repeat for Different Resistances:

• Repeat steps (iii) by selecting different resistance values (2 Ω, 3 Ω, 4 Ω, 5 Ω, and 6 Ω) on the resistance box.
• For each resistance value, record the corresponding current (I) and calculate 1/I.

(v) Organizing the Results:

• Create a table to record your measurements. Columns should include: Resistance (R), Current (I), and 1/I.

(vi) Plotting the Graph:

• Plot a graph with Resistance (R) on the vertical axis and 1/I (reciprocal of current) on the horizontal axis.

(vii) Analyzing the Graph:

• The slope (s) of the graph represents the reciprocal of the constant of proportionality in Ohm's Law (1/R).
• The y-intercept (c) of the graph should ideally be zero (assuming no internal resistance in the circuit).

Part (b): potential difference and Resistivity

(i) Potential Difference in an Electric Field

Potential difference (PD), also known as voltage, is the electrical work done per unit charge (measured in volts) between two points in an electric field. It essentially describes the energy difference between two points. Imagine it like water pressure; a higher voltage indicates a greater push for electrons to flow.

(ii) Calculating Resistivity

Resistivity (ρ) is a material's inherent property that reflects its opposition to electrical current flow. It's measured in ohm-meters (Ω⋅m). Higher resistivity indicates a greater resistance to current.

Unfortunately, we cannot calculate the battery's resistivity using the information provided. Resistivity is a property of a specific material, and the battery itself is a combination of various components. We would need the material properties of the wire used within the battery to calculate its resistivity.

However, given the wire diameter (d = 0.2 mm = 0.0002 m) and length (l = 25 cm = 0.25 m), along with the resistance (R = 7 Ω) of the wire, we can calculate its resistivity using the following formula:

ρ = R * A / l

where:

• ρ is resistivity (Ω⋅m)
• R is resistance (Ω)
• A is the cross-sectional area of the wire (m²)

To calculate the area (A) of the wire, we can use the formula for the area of a circle:

A = π * (d / 2)²

where:

• π is a mathematical constant (approximately 3.14159)
• d is the diameter of the wire (m)

Precautions for Accurate Results:

1. Ensure good connections: Double-check that all connections between components are tight and secure to avoid introducing unwanted resistance.
2. Use appropriate measuring ranges: Select ammeter and voltmeter ranges suitable for the expected current and voltage values in the circuit. Using incorrect ranges can lead to inaccurate readings.
3. Minimize external influences: Avoid placing the circuit near magnetic fields or other electrical equipment that might interfere with the measurements.

By following these steps and understanding the concepts, you should be able to perform this experiment and analyze the results effectively.

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a) (i) The root-mean-square (RMS) value of an alternating current (AC) is a measure of the effective value of the current, which is equal to the DC value that would produce the same amount of heat dissipation in a resistor. It is defined as the square root of the mean of the squares of the current values.

(ii) Impedance is the total opposition offered by a circuit to the flow of AC, and it is a complex quantity that includes both resistance and reactance. Reactance is the opposition to AC caused by the capacitance or inductance in the circuit, while resistance is the opposition to AC caused by the resistance of the conductors.

b) To find the capacitance of the capacitor, we need to use the formula for power in an AC circuit, which is given by P = VIcos(Φ). Here, V is the RMS voltage, I is the RMS current, and Φ is the phase angle between the voltage and current. If we know the power and voltage, we can calculate the current, and then use the formula for impedance (Z = V/I) to find the reactance of the capacitor. The reactance of a capacitor is given by X_C = 1/(2πfC), where f is the frequency of the AC and C is the capacitance. Solving for C, we get C = 1/(2πfX_C).

c) (i) Capacitance of a capacitor is a measure of its ability to store electrical energy in an electric field between its plates. It is defined as the ratio of the charge stored on one plate of a capacitor to the potential difference across the plates.

(ii) The total capacitance of the capacitors connected in series is given by C_total = C_1 + C_2. The potential difference across each capacitor can be found using the formula V = Q/C, where Q is the charge stored on each capacitor. If we know the potential difference across the whole circuit, we can calculate the charge stored on each capacitor, and then find the potential difference across each capacitor by dividing the charge by the capacitance.

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(i) To determine the approximate focal length, f, of the lens by focusing a distant object on the screen, follow these steps:

1. Set up the experiment by placing the ray box and screen such that the distance between the illuminated cross-wire and the screen is D = 150 cm.
2. Place the lens holder between the ray box and the screen.
3. Move the lens back and forth until a sharp image of the distant object is obtained on the screen.
4. Measure the distance, L, between the lens and the screen.
5. The approximate focal length, f, of the lens is given by the formula: f = D x L / (D + L).

(ii) To place the ray box and the screen such that the distance between the illuminated cross-wire and the screen, D = 150 cm, simply measure the distance between the two objects and adjust their positions until the distance is 150 cm.

(iii) To place the lens at a position L where a sharp image of the cross-wire is obtained on the screen, move the lens back and forth until a sharp image of the cross-wire is obtained on the screen. Measure the distance, L, between the lens and the screen.

(iv) To move the lens to obtain another sharp image of the cross-wire on the screen, simply move the lens back and forth until a sharp image of the cross-wire is obtained on the screen. Measure the distance, L, between the lens and the screen.

(v) To measure the distance, d, between L1 and L2, simply subtract the two values of L obtained in (iii) and (iv).

(vi) To evaluate D^2, d^2 and D^2 - d^2, use the values obtained in (ii) and (v) and the following formulas:

• D^2 = D x D
• d^2 = L2 x L2 - L1 x L1
• D^2 - d^2 = 4 x f x f

(vii) Repeat the procedure for four other values of D = 130cm, 100 cm, 90 cm, and 80 cm, in each case evaluate D^2, d^2, and D^2 - d^2 using the formulas in (vi).

(viii) Tabulate the results in a table with columns for D, D^2, d^2, and D^2 - d^2.

(ix) To plot a graph with D^2 - d^2 on the vertical axis

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(a)

1. Hooke's law: states that the force exerted by a spring is directly proportional to the amount it is stretched or compressed, provided that the elastic limit is not exceeded. Mathematically, it can be represented as F = kx, where F is the force applied, k is the force constant, and x is the displacement of the spring from its equilibrium position.
2. Calculation of force constant and length of the unloaded spring: First, we can calculate the force constant of the spring using the equation F = kx. Using the first length and mass, the force can be calculated as F = mg = 0.30 kg * 10 m/s² = 3 N. Substituting these values in the equation, we get 3 = k * 0.20 m. Solving for k, we get k = 15 N/m. Next, we can calculate the length of the spring when it is unloaded using the equation F = kx, where F = 0 as there is no mass hanging from the spring. Thus, kx = 0, and x = 0, which means the spring is at its equilibrium length when there is no force applied to it.

(b)

1. Diffusion: is the movement of particles or substances from an area of high concentration to an area of low concentration. This occurs until the concentration of the particles is equal throughout the system.
2. Factors affecting the rate of diffusion: Two factors that affect the rate of diffusion are the concentration gradient and the temperature. The concentration gradient refers to the difference in concentration of the particles, with a larger difference leading to a faster rate of diffusion. Higher temperature means that the particles have more energy, leading to a faster rate of diffusion.
3. Relationship between rate of diffusion and gas density: The exact relationship between the rate of diffusion of a gas and its density is not well defined. However, it can be said that the rate of diffusion of a gas is inversely proportional to its density.

(c) The relationship between the period T of orbit and R:

The equation for the period, T, of an object in orbit can be represented as T² = 4π² * R³ / (G * (M + m)), where G is the gravitational constant and M and m are the masses of the earth and satellite, respectively.

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(a) Centre of Gravity and Simple Harmonic Motion Experiment:

(i) Centre of Gravity: To determine the center of gravity of the meter rule, you need to balance it on the knife edge. The knife edge is placed vertically below the center of gravity of the meter rule. The center of gravity is the point where the weight of the object is evenly distributed and it is balanced.

(ii) Mass of the Meter Rule: The mass of the meter rule should be read from the reverse side of it and recorded.

(iii) Suspension of the Meter Rule: Suspend the meter rule by tying two parallel threads of equal length, h = 70 cm, to the 10 cm mark and the 90 cm mark of the meter rule. The meter rule should be suspended vertically.

(iv) Attaching Mass to the Meter Rule: A mass of 30g should be attached firmly to the center of gravity of the meter rule at a distance of 80 cm from the suspension point. The graduated face of the meter rule should be facing upwards.

(v) Setting the Meter Rule into Oscillation: The meter rule should be set into small angular oscillations about the vertical axis through its center of gravity by gently displacing its ends in opposite directions.

(vi) Measuring Time for 20 Oscillations: Using a stopwatch, measure the time taken for 20 oscillations and calculate the period T, T^2 and T^-2.

(vii) Repeat the Procedure for Different Values of m: Repeat the procedure for four other values of m = 40g, 50g, 60g, and 70g. In each case, determine the time for 20 oscillations and calculate T^2 and T^-2.

(viii) Plotting a Graph: Plot a graph of T on the vertical axis and m on the horizontal axis.

(ix) Determining the Slope of the Graph: Determine the slope of the graph, which is the coefficient of the linear equation that represents the graph.

(x) Evaluating Q: Calculate Q = 0.68 / s, where s is the slope of the graph.

(xi) Precautions to Ensure Accurate Results: To ensure accurate results, it is important to ensure that the meter rule is suspended vertically and that the graduated face is facing upwards. Additionally, the threads used to suspend the meter rule should be of equal length, and the knife edge should be placed vertically below the center of gravity.

(b) (i) Examples of Simple Harmonic Motion: Two examples of simple harmonic motion other than the motion of a simple pendulum are the oscillation of a mass attached to a spring and the oscillation of a body moving in a circular path.

(ii) Centre of Gravity of a Body: The center of gravity of a body is the point where the weight of the object is evenly distributed. It is the point where the object would balance if suspended from that point.

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a)

(i)

1. Focal Length: The focal length of a lens is defined as the distance between the lens and the focal point. It is the point where light rays converge after passing through the lens. The focal length is a measure of the lens's ability to converge or diverge light. A positive focal length indicates that the lens converges light to a point, while a negative focal length indicates that the lens diverges light.
2. Optical Centre: The optical centre of a lens is defined as the midpoint of the lens. It is the point through which light rays passing through the lens are undeflected.

(iii)

Ray Diagram for a Converging Lens: To produce a virtual image of an object using a converging lens, the object is placed in front of the lens at a distance greater than the focal length of the lens. Light rays from the object pass through the lens and converge at a point known as the focal point. These converged rays then diverge and form a virtual image on the same side of the lens as the object. The virtual image can be viewed by extending the diverged rays back to a point behind the lens.

b)

(i)

Primary Colors of Light: The primary colors of light are red, green, and blue. These colors of light can be combined in different ways to produce all other colors.

(ii)

Complementary Colors: The complementary color of red is green, the complementary color of green is red, and the complementary color of blue is yellow.

c)

(i)

Angle of Incidence: The angle of incidence is the angle between the incoming light ray and the surface normal (a line perpendicular to the surface) at the point of incidence. In this case, the incoming light ray strikes the surface of the prism at an angle of 60 degrees.

(ii)

Angle of Minimum Deviation: The angle of minimum deviation is the angle between the refracted light ray and the surface normal at the point of minimum deviation. In this case, the refracted light ray has a smaller angle of deviation from the surface normal than it would have at any other point within the prism. This angle can be calculated using Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media.

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To calculate the velocity of a projectile after 1 second, we need to consider both the horizontal and vertical components of its velocity.

The horizontal component of the velocity will remain constant as there are no forces acting on the projectile in the horizontal direction. The initial horizontal velocity is given as 40 m/s.

The vertical component of the velocity will change due to the effect of gravity. Gravity is always acting downwards, so it will constantly be slowing down the vertical velocity of the projectile. The vertical velocity will decrease by 10 m/s for every second that passes.

The initial vertical velocity can be calculated using the velocity and angle of launch:

v₀y = v₀ * sin(θ) = 40 * sin(30) = 20 m/s

After 1 second, the vertical velocity will be:

v₁y = v₀y - g * t = 20 - 10 * 1 = 10 m/s

So the total velocity of the projectile after 1 second will be:

v₁ = √(v₁x² + v₁y²) = √(40² + 10²) = √(1600 + 100) = √(1700) = 41 m/s

So the velocity of the projectile after 1 second is 41 m/s.

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(a)(i) The stability of a radioactive nucleus is determined by its neutron to proton ratio. If the ratio is too high or too low, the nucleus will become unstable and undergo decay. The relative stability of a nucleus is also influenced by the binding energy per nucleon, which is the energy required to separate the nucleus into its individual protons and neutrons.

(ii) To determine the order of stability of the given nuclei, X, W and Y, we need to examine their neutron to proton ratios. However, the information given is not enough to do so. We need to know the atomic numbers of these nuclei.

(b)(i) Ionization potential refers to the minimum amount of energy required to remove an electron from an atom or ion.

(ii) Information given is not enough to answer the question.

(c)(i) Work function is the minimum amount of energy required to remove an electron from a solid surface. In this case, the work function of sodium is 2.0 eV, meaning that 2.0 eV of energy is required to remove an electron from the surface of a sodium metal.

(ii) The energy of light can be calculated using the formula E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the light. The energy of the light in this case is 1.97 eV. If the energy of the light is greater than the work function of sodium, which is 2.0 eV, photoelectrons will be emitted. In this case, the energy of the light is not enough to remove electrons from the surface of sodium, so photoelectrons will not be emitted.