WAEC SSCE - Physics - 2013

At which position should an object be placed in front of a concave mirror in order to obtain an image which is of the same size as the object?

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The slope of a linear distance-times graph represents

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The slope of a linear distance-time graph represents the object's speed or rate of change of distance with respect to time. In other words, the slope is a measure of how fast the object is moving. A steeper slope indicates a faster speed, while a shallower slope indicates a slower speed. Therefore, the correct answer is speed.

Which of the following devices does not makes use of eddy current for its action? A/An

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A body of mass 20g projected vertically upwards in vacuum returns to the point of projection after 1.2s. [g = 10ms^-2]. Determine the potential energy of the body at the maximum height of its motion

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To determine the potential energy of the body at the maximum height of its motion, we need to follow these steps:

1. Calculate the speed of projection (initial velocity): From the previous solution, we determined that the speed of projection $uu$ is 6 m/s.

2. Determine the maximum height: Use the kinematic equation for the vertical motion to find the maximum height:

   $v^2=u^2-2ghv^2\; =\; u^2\; -\; 2gh$

   At the maximum height, the final velocity $vv$ is 0, so:

   $0=u^2-2gh⟹h=\frac{u^2}{2g}0\; =\; u^2\; -\; 2gh\; \backslash implies\; h\; =\; \backslash frac\{u^2\}\{2g\}$

   Substituting $u=6\text{ m/s}u\; =\; 6\; \backslash text\{\; m/s\}$ and $g=10{\text{ m/s}}^{2}g\; =\; 10\; \backslash text\{\; m/s\}^2$:

   $h=\frac{(6\text{ m/s}{)}^2}{2\times 10{\text{ m/s}}^2}=\frac{36{\text{ m}}^2\mathrm{/}{\text{s}}^2}{20{\text{ m/s}}^2}=1.8\text{ m}h\; =\; \backslash frac\{(6\; \backslash text\{\; m/s\})^2\}\{2\; \backslash times\; 10\; \backslash text\{\; m/s\}^2\}\; =\; \backslash frac\{36\; \backslash text\{\; m\}^2/\backslash text\{s\}^2\}\{20\; \backslash text\{\; m/s\}^2\}\; =\; 1.8\; \backslash text\{\; m\}$

3. Calculate the potential energy (PE): The potential energy at the maximum height is given by:

   $\text{PE}=mgh\backslash text\{PE\}\; =\; mgh$

   Convert the mass from grams to kilograms:

   $m=20\text{ g}=0.02\text{ kg}m\; =\; 20\; \backslash text\{\; g\}\; =\; 0.02\; \backslash text\{\; kg\}$

   Now substitute $m=0.02\text{ kg}m\; =\; 0.02\; \backslash text\{\; kg\}$, $g=10{\text{ m/s}}^{2}g\; =\; 10\; \backslash text\{\; m/s\}^2$, and $h=1.8\text{ m}h\; =\; 1.8\; \backslash text\{\; m\}$:

   $\text{PE}=0.02\text{ kg}\times 10{\text{ m/s}}^2\times 1.8\text{ m}=0.36\text{ J}\backslash text\{PE\}\; =\; 0.02\; \backslash text\{\; kg\}\; \backslash times\; 10\; \backslash text\{\; m/s\}^2\; \backslash times\; 1.8\; \backslash text\{\; m\}\; =\; 0.36\; \backslash text\{\; J\}$

Therefore, the potential energy of the body at the maximum height of its motion is $\boxed{{\displaystyle 0.36\text{ J}}}\backslash boxed\{0.36\; \backslash text\{\; J\}\}$

The diagram above illustrates a waveform. Which of the point on the waveform are in phase?

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Four co-planar forces of magnitudes 10N, 17N, 6N and 20N act at point O as shown in the above diagram. Determine the magnitude of the resultant force

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A potential difference of 12V is applied across the ends of a 6\(\Omega\) resistor for 10 minutes. Determine the quantity of heat generated

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The capacitance of parallel plates capacitors varies

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A string under tension produces a note of frequency 14Hz. Determine the frequency when the tension is quadrupled.

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The frequency of a note produced by a string under tension is directly proportional to the square root of the tension. This relationship is given by the equation: f = (1/2L) √(T/μ) Where f is the frequency, T is the tension, L is the length of the string and μ is the linear mass density of the string. Since the length and mass density of the string are constant, we can say that the frequency is directly proportional to the square root of the tension: f ∝ √T So, if we quadruple the tension, the frequency will double. Therefore, the frequency produced by the string when the tension is quadrupled will be: f' = 2f = 2 × 14Hz = 28Hz Therefore, the correct answer is 28Hz.

The maximum displacement on either side of the equilibrium position of an object in simple harmonic motion represents

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The maximum displacement on either side of the equilibrium position of an object in simple harmonic motion represents its **amplitude**. In simple harmonic motion, the object oscillates back and forth around a central point, which is its equilibrium position. The amplitude is the maximum displacement of the object from this equilibrium position, in either direction. It represents the "strength" or "size" of the oscillation. The other options are not correct: the **period** is the time it takes for one complete oscillation, the **wavelength** is the distance between two adjacent points in a wave that are in phase, and the **frequency** is the number of oscillations per unit time (usually measured in Hertz).

The refractive index of a material is 1.5. Calculate the critical angle at the glass-air interface

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The critical angle is the angle of incidence at which the angle of refraction is 90 degrees. Using Snell's law, we can relate the critical angle to the refractive index. At the critical angle, the sine of the angle of refraction is 1, so we can write: sin(critical angle) = 1/n where n is the refractive index. Substituting n=1.5 gives: sin(critical angle) = 1/1.5 = 0.67 Taking the inverse sine of both sides gives: critical angle = sin^-1(0.67) = 42^o Therefore, the correct answer is 42^o.

The volume of a given mass of gas at 27^oC and 800 mmHg is 76cm². Calculate its volume at s.t.p

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The velocity ratio of an inclined plane

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The velocity ratio of an inclined plane is a measure of the effectiveness of the plane in reducing the force required to move an object to a certain height. It is defined as the ratio of the distance moved by the load to the distance moved by the effort. The velocity ratio of an inclined plane is dependent on the angle of inclination. As the angle of inclination increases, the velocity ratio also increases. This means that a steeper inclined plane is more effective at reducing the force required to move an object to a certain height. Therefore, the correct option is: increases with increase in the angle of inclination.

An electric heater has a resistance of 50\(\Omega\). When it is immersed in water and connected to mains source, it draws a current of 4.0A. Calculate the heat gained by the water if the heater is switched on for 2 minutes, assuming no heat losses to the surroundings

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The heat gained by the water can be calculated using the formula: Heat = Power × Time where Power = Current × Voltage and Time = 2 minutes = 120 seconds The voltage can be calculated using Ohm's law: Voltage = Current × Resistance Substituting the values given: Voltage = 4.0A × 50\(\Omega\) = 200V Therefore, Power = 4.0A × 200V = 800W Substituting the values in the formula: Heat = Power × Time = 800W × 120s = 96,000J Therefore, the heat gained by the water is 96,000J. The correct option is (d) 96,000J.

Which of the following statements about waves in pipes is correct?

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The minimum energy required to cause photoelectric emission when the surface of a metal is irradiated with electromagnetic radiation of suitable frequency is called

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The minimum energy required to cause photoelectric emission when the surface of a metal is irradiated with electromagnetic radiation of suitable frequency is called the work function. It is the amount of energy required to remove an electron from the metal surface, overcoming the attractive forces holding the electron in the metal. The energy of the incident photon must be greater than or equal to the work function for photoelectric emission to occur. If the energy of the incident photon is less than the work function, no electrons will be emitted.

Which of the following types of thermometer is used for the calibration of other thermometers?

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The type of thermometer used for the calibration of other thermometers is the constant volume gas thermometer. This thermometer operates on the principle of the ideal gas law, which states that the pressure and volume of a gas are proportional to its absolute temperature. In a constant volume gas thermometer, a gas is trapped in a container with a fixed volume, and its pressure is measured at different temperatures to obtain a calibration curve. This curve can then be used to calibrate other types of thermometers, such as liquid-in-glass thermometers or thermocouples. Therefore, the correct answer is constant volume gas thermometer.

Which of the following units is equivalent to the watt?

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The unit of power is the watt (W), which is defined as the rate at which work is done or energy is transferred. In terms of fundamental units, power can be expressed as the product of force and velocity, which can be further expressed as mass times acceleration times velocity. Simplifying this expression, we get the unit of power as kgm²s^-3, which is option B.

Which of the following statements about the use of radioisotopes is not correct? They are used to

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The statement that radioisotopes are used to induce mutations in plants and animals to obtain new and improved varieties is not correct. Radioisotopes are unstable isotopes of an element that emit radiation as they undergo decay, and they have several applications in various fields. However, inducing mutations in plants and animals is not one of them. Instead, mutagenic agents like chemicals or radiation are used for this purpose. Radioisotopes are used to trace the paths of metabolic processes in plants and animals, estimate the age of rocks, locate broken bones, and several other applications in fields such as medicine, agriculture, and industry.

An electric circuit is connected as illustrated above. Determine the equivalent e.m.f and current flowing through the circuit respectively, neglecting the internal resistance of the cells

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The rising of a liquid in an open and ended glass tube of narrow bore is

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The rising of a liquid in an open and ended glass tube of narrow bore is called capillarity. Capillarity is the result of the combination of adhesive and cohesive forces between the liquid molecules and the molecules of the tube material. In a narrow tube, the adhesive forces between the liquid and the tube are stronger than the cohesive forces between the liquid molecules themselves, causing the liquid to rise in the tube. The narrower the tube, the higher the liquid rises due to capillary action.

The total area under a force-velocity graph represents

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Which of the following statements about the Galilean telescope is not correct?

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The correct option is: "the final image is inverted". This statement is incorrect. The Galilean telescope consists of a converging lens (the objective lens) and a diverging lens (the eyepiece) placed at a distance equal to the sum of their focal lengths. The objective lens produces a real and inverted image of the object being observed, which is then magnified and made upright by the eyepiece lens. So, the final image is upright. The other options are: - "it is shorter than terrestial telescope" - This statement is correct. The Galilean telescope is shorter than the terrestrial telescope, as it uses a combination of lenses to produce a magnified image rather than a long focal length objective lens. - "it has a small field of view" - This statement is generally correct. The Galilean telescope has a smaller field of view compared to the terrestrial telescope due to its design, which results in a narrow angle of view. - "the final image is erect" - This statement is correct. As mentioned earlier, the final image produced by a Galilean telescope is upright or erect.

Images formed by a convex mirror are always

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Images formed by a convex mirror are always behind the mirror, real, and upright. However, the images are always smaller than the actual object. This is due to the fact that convex mirrors cause light rays to diverge, making the image appear farther away and smaller than it actually is. Therefore, the correct option in this case would be "behind the mirror".

A coil of inductance 0.12 H and resistance 4\(\Omega\), is connected across a 240V, 50Hz supply. Calculate the current through it. [\(\pi\) = 3.142]

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We can use the formula for the current in an AC circuit with an inductor and a resistor: \begin{equation*} I = \frac{V}{\sqrt{R^2 + (\omega L)^2}} \end{equation*} where V is the voltage, R is the resistance, L is the inductance, and \(\omega\) is the angular frequency. We can find \(\omega\) using the formula: \begin{equation*} \omega = 2\pi f \end{equation*} where f is the frequency. Substituting the given values, we get: \begin{align*} \omega &= 2\pi \times 50\text{ Hz} \\ &= 100\pi\text{ rad/s} \end{align*} Now we can substitute all the values into the first formula: \begin{align*} I &= \frac{V}{\sqrt{R^2 + (\omega L)^2}} \\ &= \frac{240\text{ V}}{\sqrt{(4\Omega)^2 + (100\pi \text{ rad/s} \times 0.12\text{ H})^2}} \\ &\approx 6.3\text{ A} \end{align*} Therefore, the current through the coil is approximately 6.3A. Answer is correct.

The outlet of a bicycle pump is used to inflate a football as illustrated in the diagram above. Why does the pressure of the air inside the pump increases as the pump handle is slowly pushed downward at constant temperature?

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As the pump handle is slowly pushed downwards, the volume of the pump is reduced. This means that the same amount of air inside the pump is now occupying a smaller space. Since the temperature is constant, the increase in pressure results from an increase in the frequency of collisions of air molecules with the walls of the pump. The air molecules are being compressed into a smaller volume, leading to an increase in pressure. Therefore, the correct answer is: the frequency of collision of the air molecules with the walls of the pump is increased.

Ice of mass 10g at 5°C was completely converted to water at 0°C, calculate the quantity of heat used. [specific heat capacity of ice = 2.1 Jg\(^{-1}\)K\(^{-1}\), specific latent heat of fusion of ice = 336 Jg\(^{-1}\)]

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From Newton's first law of motion,

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Which of the following radiations has it's frequency lower than that of infrared radiation?

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Radio waves have frequencies lower than infrared radiation. Radio waves have the lowest frequency among all the electromagnetic radiations, ranging from a few hertz to several gigahertz. On the other hand, infrared radiation has a frequency range of about 430 THz to 300 GHz. Therefore, radio waves have a lower frequency than infrared radiation.

Which of the following statements about pressure in a liquid is correct?

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The correct statement about pressure in a liquid is "the pressure in a liquid increases with depth." This means that as the depth of a liquid increases, the pressure at that point also increases. This is because the weight of the liquid above a certain depth creates a force that increases the pressure at that depth. The higher the density of a liquid, the higher the pressure it exerts, which means that the second statement is incorrect. The third statement is also incorrect because pressure in a liquid acts in all directions, not just perpendicular to the sides of the containing vessel. Finally, the fourth statement is also incorrect because pressure in a liquid is affected by the acceleration due to gravity, as the weight of the liquid above a certain depth creates a force that increases the pressure at that depth.

Which of the following instruments is used to determine the accurate value of the electromotive force of a cell?

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The instrument used to determine the accurate value of the electromotive force (emf) of a cell is called a potentiometer. A potentiometer measures the potential difference across a known length of a uniform wire and compares it with the potential difference across the unknown emf source, which is connected in parallel with the wire. By adjusting the length of the wire until the potential difference across the known length is equal to the potential difference across the cell, the emf of the cell can be determined accurately. Therefore, the correct option is a potentiometer.

A body of mass 2kg is released from rest on a plane inclined at an angle of 60° to the horizontal. Calculate the acceleration of the body down the plane.[g = 10ms\(^{-2}\)]

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When a body of mass m is released on an inclined plane at an angle θ to the horizontal, the component of its weight acting down the plane is mgsinθ. The force acting parallel to the plane that causes the body to slide down is given by F = mgsinθ. The acceleration of the body down the plane is given by a = F/m = gsinθ. In this case, m = 2kg and θ = 60°. Therefore, the acceleration of the body down the plane is given by: a = gsinθ = 10ms\(^{-2}\) x sin(60°) = 8.7ms\(^{-2}\) Therefore, the correct answer is 8.7ms\(^{-2}\).

When a person holds a negatively charges metal rod and stands bare-footed on the ground, how will the charges leak?

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When a person holds a negatively charged metal rod and stands bare-footed on the ground, the negative charges will flow to the ground through the person's body. This is because the human body is a good conductor of electricity, allowing charges to flow easily through it. When a person is standing on the ground, they are in contact with a large conductive surface (the earth), which provides a pathway for the charges to flow away from the person's body and into the ground. This process is called grounding or earthing, and it helps to prevent the buildup of static electricity on the person's body.

Which of the following phenomena supports the theory that waves have a particle nature?

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The phenomenon that supports the theory that waves have a particle nature is the "photoelectric effect." This effect demonstrates that light behaves as a stream of particles, called photons, which transfer their energy to electrons in a metal surface. When the energy of a photon exceeds a certain threshold value, an electron is ejected from the metal surface. This effect cannot be explained by wave theory alone, but it can be explained by assuming that light has a particle nature. Therefore, the photoelectric effect provides strong evidence for the wave-particle duality of light.

When salt is dissolved in water, the freezing point of the water

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When salt is dissolved in water, it lowers the freezing point of the water. This is because adding salt lowers the temperature at which water freezes, a process known as freezing point depression. When salt is added to water, it lowers the freezing point of the water because the salt ions interfere with the formation of ice crystals. The result is that the saltwater mixture will remain in a liquid state at a lower temperature than pure water would. Therefore, the correct option is "decreases".

Solid friction, like viscosity is

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Solid friction is in opposition to motion. When two solid surfaces are in contact, there is a force that resists the relative motion between them, known as friction. In the case of solid friction, this force acts perpendicular to the surfaces in contact and depends on the normal reaction between them, which is the force exerted by one surface on the other perpendicular to the contact area. Friction is also independent of the surface area in contact and dependent on the relative motion between the layers.

A body of mass 11kg is suspended from a ceiling fan by an aluminum wire of length 2m and diameter 2mm. Calculate the elastic energy stored in the wire [Young's modulus of aluminum is 7.0 x 10¹⁰Nm^-2, g = 10ms^-2, \(\pi\) = 3.142]`

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A charge of 2.0 x 10\(^{-5}\) C experiences a force of 80N in a uniform electric field. Calculate the magnitude of the electric field intensity

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The electric field intensity (E) is defined as the force per unit charge. Therefore, we can find E by dividing the force (F) by the charge (q). E = F/q Substituting the given values, we have: E = 80N / (2.0 x 10\(^{-5}\) C) E = 4.0 x 10\(^6\) NC\(^{-1}\) Therefore, the magnitude of the electric field intensity is 4.0 x 10\(^6\) NC\(^{-1}\). So, the correct option is (B) 4.0 x 10⁶ NC^-1.

A block of wood of mass 5kg is pulled on a platform by a force of 40N as illustrated in the diagram above. If the frictional force, F experienced by the block is 12N, calculate the magnitude of the acceleration of the acceleration of the block

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To calculate the acceleration of the block, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. Mathematically, this is expressed as a = F_net/m, where a is the acceleration, F_net is the net force, and m is the mass of the object. In this problem, the net force acting on the block is the difference between the applied force and the frictional force, i.e., F_net = F_applied - F_friction = 40N - 12N = 28N. Therefore, the acceleration of the block is a = F_net/m = 28N/5kg = 5.6ms^-2. Therefore, the correct option is 5.6ms^-2.

A diverging lens of focal length 30cm produces an image 20cm from the lens. Determine the object distance

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The magnitude of the expansion or contraction of a substance depends on the i. temperature change ii. nature of the substance iii. size of the substance. Which of the statements above are correct?

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The correct statement is (i and ii only). The magnitude of expansion or contraction of a substance depends on the temperature change and the nature of the substance. The size of the substance does not affect the magnitude of the expansion or contraction. When a substance is heated, its temperature increases, and the particles in the substance gain kinetic energy, leading to an increase in the space between the particles. This increase in space between the particles results in expansion of the substance. The nature of the substance also plays a role in determining the magnitude of expansion or contraction. Different substances have different coefficients of thermal expansion, which is a measure of how much a substance expands or contracts when its temperature changes. Some substances expand more than others when they are heated and contract more than others when they are cooled.

The work function of a metal is 2.56 x 10^-19J. Calculate the frequency of a photon whose energy is required to eject from the metal an electron with kinetic energy of 3.0ev. [1 eV = 1.6 x 10^-19J, h = 6.6 x 10^-34Js]

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The energy required to eject an electron from a metal is given by: Kinetic energy of ejected electron = Energy of photon – Work function We can rearrange this equation to find the energy of the photon: Energy of photon = Kinetic energy of ejected electron + Work function The kinetic energy of the ejected electron is given as 3.0 eV. We can convert this to joules using the conversion factor 1 eV = 1.6 x 10^-19 J: Kinetic energy of ejected electron = 3.0 eV x 1.6 x 10^-19 J/eV = 4.8 x 10^-19 J Substituting this value and the given work function into the equation for the energy of the photon: Energy of photon = 4.8 x 10^-19 J + 2.56 x 10^-19 J = 7.36 x 10^-19 J We can use the formula E = hf to relate the energy of the photon to its frequency f: E = hf where h is Planck's constant, h = 6.6 x 10^-34 J s. Rearranging the equation gives: f = E/h Substituting the values we obtained: f = (7.36 x 10^-19 J) / (6.6 x 10^-34 J s) ≈ 1.12 x 10¹⁵ Hz Therefore, the frequency of the photon required to eject an electron with a kinetic energy of 3.0 eV from a metal with a work function of 2.56 x 10^-19 J is approximately 1.12 x 10¹⁵ Hz.

A body of mass 20g projected vertically upwards in vacuum returns to the point of projection after 1.2s. [g = 10ms\(^{-2}\)]. Calculate the speed of projection

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To determine the speed of projection of a body projected vertically upwards in a vacuum, we can use the principles of kinematics and the given information. Here are the steps:

1. Understand the total time of flight: The total time taken for the body to go up and come back down is 1.2 seconds.

2. Determine the time to reach the maximum height: Since the time to go up is equal to the time to come down, the time to reach the maximum height is half of the total time of flight.

   $t_{\text{up}}=\frac{1.2\text{ s}}{2}=0.6\text{ s}t\_\{\backslash text\{up\}\}\; =\; \backslash frac\{1.2\; \backslash text\{\; s\}\}\{2\}\; =\; 0.6\; \backslash text\{\; s\}$

3. Use the kinematic equation for velocity: The velocity at the maximum height is 0 (since the body momentarily stops before falling back down). We can use the equation:

   $v=u-gtv\; =\; u\; -\; gt$

   where $vv$ is the final velocity (0 m/s at the maximum height), $uu$ is the initial velocity (speed of projection), $gg$ is the acceleration due to gravity (10 m/s²), and $tt$ is the time taken to reach the maximum height (0.6 s).

   Setting $v=0v\; =\; 0$:

   $0=u-g\cdot t0\; =\; u\; -\; g\; \backslash cdot\; t$

4. Solve for $uu$:

   $u=g\cdot t=10{\text{ m/s}}^2\cdot 0.6\text{ s}=6\text{ m/s}u\; =\; g\; \backslash cdot\; t\; =\; 10\; \backslash text\{\; m/s\}^2\; \backslash cdot\; 0.6\; \backslash text\{\; s\}\; =\; 6\; \backslash text\{\; m/s\}$

Therefore, the speed of projection is $\boxed{{\displaystyle 6.0\text{ m/s}}}\backslash boxed\{6.0\; \backslash text\{\; m/s\}\}$6.0 m/s

The equation of a certain progressive transverse wave is y = 2 sin 2 \(\pi ( \frac{t}{0.01} - \frac{x}{30})\), where x and y are in cm and t in seconds. Calculate the period of the wave.

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The general equation of a progressive transverse wave is given by: y = A sin (kx - ωt) where A is the amplitude, k is the wave number, x is the position of the particle, ω is the angular frequency, and t is the time. Comparing this equation with the given equation, we have: A = 2 cm k = 2π/30 cm^(-1) = π/15 cm^(-1) ω = 2π/T, where T is the period Thus, we have: ω = 2π/T = 2π/(0.01 s) Substituting the value of ω, we get: 2π/(0.01 s) = π/15 cm^(-1) Simplifying this equation, we get: T = 0.01 s Therefore, the period of the wave is 0.01 s.

Which of the following particles are termed nucleons in a neutral atom?

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In a neutral atom, the number of positively charged protons in the nucleus is equal to the number of negatively charged electrons surrounding the nucleus. The nucleons in an atom refer to the particles present in the nucleus, which are protons and neutrons. Therefore, the correct answer is (a) protons and neutrons.

Highly polished silvery surfaces are

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(a) Define ionization potential.

(b)(i) State the three types of emission spectra.

(ii) Name one source each which produces each of the spectra stated in (b)(i).

(c) In an x-ray tube, electrons are accelerated the target by a potential difference of 80 A Calculate the:

(i) speed of the electron;

ii) threshold wavelength of the electron. [h=6.6 x 10\(^{-34}\) Js; e = 1.6 x 10\(^{-19}\) C; Me = 9.1 x 10\(^{-31}\)

d) An x-ray photon of frequency 4.5 x 10\(^{-18}\) strikes an. electron, assumed to be at rest. If t electron absorbs all the photon energy, calculate the speed acquired by the electron. [ h = 6.6 x 10\(^{-34}\) Js; Me = 9.1 x 10\(^{-31}\) kg ]

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TEST OF PRACTICAL KNOWLEDGE QUESTION

You are provided with a uniform metre rule of mass, M indicated on its reverse side, a knife-edge, a graduated measuring cylinder of known mass, M\(_{1}\) marked on it and other necessary apparatus.

1. Read and record with values of M and m\(_{1}\). 
2. Balance the metre rule horizontally on the knife edge. Read and record the balance point as G.
3. Tie a loop of thread around the neck of the measuring cylinder.
4. Fill the cylinder with the sand provided to the 2cm\(^{3}\) mark. Record the volume, V, of the sand.
5. Hang the cylinder at the 2 cm mark of the metre rule and adjust the position of the knife edge until the rule balances horizontally.
6. Read and record the new balance position K.
7. Determine the value of e and f.
8. Determine the mass, m\(_{2}\), of the sand in the measuring cylinder. Hint: m\(_{2}\) = (\(\frac{\text {M x f}}{e}\)) - m\(_{1}\).
9. Repeat the procedure by filling the measuring cylinder to the mark V = 4,6,8 and 10 cm\(^{3}\). In each case, ensure that the measuring cylinder is kept constant at the 2 cm mark on the metre rule.
10. Tabulate your readings.
11. Plot a graph with m\(_{2}\) on the vertical axis and V on the horizontal axis.
12. Determine the slope, s, of the graph.
13. State two precautions taken to ensure accurate results.

(b)i. Determine the mass of 7.5 cm\(^{3}\) of the sand using your graph.

ii. A gold coin of mass 102.0 g has a uniform cross-sectional area of 10.0 cm\(^{2}\). Calculate its thickness. [Density of gold=19.3 g cm\(^{-3}\)]

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(a) Define boiling point of a liquid.

(b) Describe how water in a round bottom flask could be made to boil without heating it. [diagram not necessary]

(c) State three applications of expansion of metals.

(d) A room with floor measurements 7m x 10 m contains air of mass 250 kg at a temperature of 34°C. The air is cooled until the temperature falls to 24°C. Calculate the: (i) height of the room;

(ii) quantity of energy extracted to cool the room;

(iii) which is higher: the calculated value or the actual energy needed to cool the room? Give a reason for your answer. [ Specific heat capacity of air = 1010 Jkg\(^{-1}\)K\(^{-1}\); density of air = 1.25 kg m\(^{-3}]

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(a) On which day would sound wave travel faster: on a hot or cold day? Explain.

(b) Why are megaphones shaped like funnels?

(c) A ray of light is incident on a surface of a ectangular glass prism of refractive index 1.5 illustrated in the diagram below.

(i) Copy the diagram a label the angles of: (\(\alpha\)) Incidence (x); (\(\beta\)) Reflection (y); (\(\gamma\)) refraction (z); with t glass letters indicated.

(ii) Calculate the angle refraction to the nearest whole number.

(d) A sonomesr wire vibrates in simple harmoi motion with a maximum amplitude of 1.0 cm. Calculate the frequency of vibration of the wire, giv that the magnitade of the maximum acceleration of the wire is 980ms\(^{-2}\). [\(\pi \frac{22}{7}\)]

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(a) State the triangle law of vector addition.

(b) Name the four physical quantities that are associated with the equationq of linear motion.

(c) Using the same set of axes, sketch and label two graphs to illustrate the variation of potential energy and kinetic energy with time for a body in simple harmonic motion.

(d)

A light spiral spring of force constant K lies on a horizontal frictionless surface and has one end fixed to a vertical wall. A block P of mass 2.0 kg placed against the free end of the spring is pushed a distance 5 cm towards the wall with 10J of energy as illustrated in the diagram above. The block is released and after 0.25s, it collides inelastically with a stationary block Q of mass 4.0 kg. Calculate the:

(i) value of k;

(ii) force used to compress the spring;

(iii) acceleration of the block p after release;

(iv) common speed after collision of the blocks.

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Name the three basic components P, Q and R that make up a cathode ray tube, as illustrated in the diagram above

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Write down the name of:

(a) two particles used in explaining the wave nature of matter;

(b) one device whose invention is based on the wave nature of matter.

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(a) what is Brownian motion?

(b) State the two inferences that can be drawn from Brownian motion experiment.

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The accelerating potential in a cathode ray oscilloscope is 2.5 kV. Calculate the maximum speed of the accelerated electrons. [ e = 1.6 x 10\(^{-19}\) C; Me = 9.1 x 10\(^{-31}\) kg]

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A projectile is released with a speed u at an angle \(\theta\) to the horizontal. With the aid of a diagram, show that the time of flight is equal to \(\frac{2uSin\theta}{g}\), where g is the acceleration of free fall.

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TEST OF PRACTICAL KNOWLEDGE QUESTION

Using the diagram above as a guide, carry out the following instructions:

1. Fix a plain sheet of paper on the Celotex board.
2. Place the rectangular glass prism on the paper and trace its outline, ABCD. Remove the prism.
3. Draw a normal NMP to meet AB and DC at M and P respectively such that |AM|=DP=2.0cm.
4. Trace the ray PQ with two pins, P\(_{1}\) and P\(_{2}\) at P and Q respectively such that angle MPQ = i =50º 
5. Replace the prism on its outline. Trace the emergent ray with two other pins P\(_{3}\) and P\(_{4}\) such that they lie in a straight line with P\(_{2}\) and the image of P\(_{1}\) viewed through the glass prism.
6. Measure and record \(\theta\), the angle between the emergent ray and face AB of the glass prism.
7. Evaluate cos \(\theta\) and sin i.
8. Repeat the procedure for four other values of i = 10°, 15°,20° and25°.
9. Tabulate your readings.
10. Plot a graph with cos \(\theta\) on the vertical axis and sin i on the horizontal axis.
11. Determine the slope, s, of the graph
12. State two precautions taken to ensure accurate results. Attach your traces to your answer booklet 

(b)i. State the laws of refraction of light

ii. Explain what is meant by the statement the refractive index of a material is 1.65

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A mass of 11.0 kg is suspended from a rigid support by an aluminum wire of length 2.0 m, diameter 2.0 mm and Young's modulus 7.0 x 10\(^{11}\) Nm\(^{-2}\). Determine the extension produced. [g = 10 ms\(^{-2}\); \(\pi\) = 3.142]

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TEST OF PRACTICAL KNOWLEDGE QUESTION

You are provided with a constantan wire, a2 \(\Omega\)standard resistor, an accumulator E, an ammeter A, a key K, and other necessary apparatus.

1. Measure and record the emf of the accumulator provided
2. Connect a circuit as shown in the diagram above.
3. Close the key, read and record the ammeter reading l\(_{o}\) when the crocodile clip is not in contact with the Constantan wire.
4. Open the key with the clip making contact with the wire, when d=90cm, close the key. Read and record the ammeter reading l.
5. Evaluate d\(^{_1}\)
6. Repeat the procedure for four other values of d=80, 70, 60, and 50 cm
7. In each case, read and record the ammeter reading and evaluatre d\(^{_1}\).
8. Tabulate your readings.
9. Plot a graph with I on the vertical axis and d\(^{_1}\) on the horizontal aXIS.
10. Determine the slope, S of the graph and its intercept, c, on the vertical axis.
11. Evaluate k = \(\frac{c}{s}\)
12. Using your graph, determine the current I when d=55cm.
13. State two precautions taken to obtain accurate results.

(b)i. Explain what is meant by the potential difference between two points in an electric circuit.

ii.  State two factors on which the resistance of a wire depends.

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(a) What is a polarizer?

(b) With the aid of a diagram, explain how a polarizer can be used to polarize a beam of unpolarized light.

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(a) Explain briefly the purpose of earthing electrical appliance.

(b) Why does the light frorr bulb connected to a simple cell dim and eventually goes off after a while?

(c) A coil of incidence 0.007 H, a resistor of resistance 8 \(\Omega\) and a capacitor capacitance 0.001 F are connected in series an a.c. source of frequency \(\frac{500}{\pi}\)Hz. If the r.m.s voltages across the coil, the resistor and capacitor are 30v, 20v and 70v respectively;

(i) draw a vector diagram to illustrate the voltage across the components in the circuit.

(ii) Calculate the: (\(\alpha\)) r.m.s voltage of the source

(\(\beta\)) r.m.s current in the circuit;

(\(\gamma\)) power dissipated in the circuit.

iii) write down the sinusoidal equation for the r.m.s voltage, V, in terms of the time, t.

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