WAEC SSCE - Physics - 2009

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The period of a simple pendulum depends on its length. The relationship between the period (T) of a simple pendulum and its length (L) is given by the formula: T = 2π√(L/g), where g is the acceleration due to gravity. If the period of the pendulum doubles, then the new period (T') is twice the original period (T): T' = 2T = 4π√(L/g). If the length of the pendulum is increased by X, then the new length (L') is: L' = L + X. Substituting this into the formula for the new period gives: T' = 2π√((L+X)/g) Since T' = 2T, we can equate the two expressions for T' and simplify: 4π√(L/g) = 2π√((L+X)/g) Squaring both sides and canceling the common factor of 4π²/g, we get: L = (L+X)/2 Solving for X gives: X = L Therefore, the length of the pendulum needs to be increased by 80.0 cm to double its period, so X = 80.0 cm. The answer is option D: 240.0 cm.

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The increase in length of the rod can be calculated using the formula: ΔL = αLΔT where: ΔL = change in length α = linear expansivity coefficient L = initial length ΔT = change in temperature Substituting the given values, we have: ΔL = (4.0 x 10^-3 K^-1) x (2m) x (80°C - 25°C) ΔL = 0.44m Therefore, the increase in length of the rod is 0.44m. Note: When a material is heated, its length increases due to the expansion of its particles. The linear expansivity coefficient (α) represents the fractional change in length per unit change in temperature.

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A concave mirror forms an image of an object when light rays from the object are reflected off the mirror. The image formed can either be magnified or reduced in size, and it can be erect or inverted depending on where the object is placed in relation to the mirror. In this question, we are told that the concave mirror forms a magnified and erect image. For this to happen, the object must be placed between the focus and the pole of the mirror. This is because, in a concave mirror, light rays coming parallel to the principal axis are reflected and converge at the focus. When an object is placed between the focus and the pole of the mirror, the reflected rays will still converge and form a real image that is magnified and erect. If the object is placed at the focus, the reflected rays will be parallel, and no image will be formed. If the object is placed beyond the radius of curvature, the image formed will be real, but it will be inverted. If the object is placed at the center of curvature, the image formed will be real, inverted, and the same size as the object.

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When a pair of equal and opposite non-collinear parallel forces act on a body, a rotational motion will be produced. This is because the two forces will cause a torque or moment about the center of mass of the body, which will result in the body rotating around that point. The magnitude of the torque is proportional to the product of the forces and the perpendicular distance between them, which is also known as the lever arm. Therefore, the greater the force or the longer the lever arm, the greater the torque and the faster the body will rotate. The other options, such as vibrational motion, random motion, and translational motion, do not apply in this scenario because the forces are not acting in such a way as to cause those types of motion.

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When two forces act on a body, their resultant force can be calculated using vector addition. The equilibrant is the force required to balance the two forces and bring the body into a state of equilibrium. It has the same magnitude as the resultant force but acts in the opposite direction. To calculate the equilibrant, we need to find the resultant force of the two given forces. We can do this by drawing a vector diagram or using trigonometry. Using trigonometry, we can find the magnitude of the resultant force as follows: \begin{align*} F_{\text{resultant}} &= \sqrt{(6\text{N})^2 + (8\text{N})^2} \\ &= \sqrt{36\text{N}^2 + 64\text{N}^2} \\ &= \sqrt{100\text{N}^2} \\ &= 10\text{N} \end{align*} The equilibrant has the same magnitude as the resultant force but acts in the opposite direction. Therefore, the magnitude of the equilibrant is also 10N. So, the correct answer is 10N.

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The maximum displacement of a vibrating tuning fork is its amplitude. In a vibrating system, amplitude refers to the maximum displacement of the vibrating object from its equilibrium or rest position. For a tuning fork, the amplitude refers to the maximum distance that the prongs of the fork move away from their resting position when they are vibrating. The amplitude of a tuning fork determines the intensity or loudness of the sound it produces. A larger amplitude produces a louder sound, while a smaller amplitude produces a softer sound. Therefore, the correct option is "amplitude".

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The internal resistance of a cell can be calculated using the equation: r = (E - V)/I where r is the internal resistance of the cell, E is the e.m.f. of the cell, V is the voltage across the cell, and I is the current passing through the circuit. In this case, the e.m.f. of the cell is given as 1.5V, and the resistance of the resistor is 3.0\(\Omega\). Since the cell and the resistor are connected in series, the current passing through them will be the same. We can calculate the current using Ohm's law: I = V/R = 0.9V/3.0\(\Omega\) = 0.3A Now we can use the formula for the internal resistance: r = (E - V)/I = (1.5V - 0.9V)/0.3A = 2.0\(\Omega\) Therefore, the internal resistance of the cell is 2.0\(\Omega\). Answer option A is correct.

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The instrument used to measure relative humidity is called a hygrometer. A hygrometer is a device that measures the amount of water vapor in the air or the humidity level. It measures the amount of moisture in the air by using two thermometers. One of the thermometers is dry while the other is kept wet. The difference in temperature between the two thermometers is then measured, and this difference is used to calculate the relative humidity of the air. Therefore, the correct option is (d) hygrometer.

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The numbers 238 and 235 represent the nucleon numbers of the two isotopes of uranium, namely \(^{238}U\) and \(^{235}U\). The nucleon number represents the total number of protons and neutrons in the nucleus of an atom. Therefore, \(^{238}U\) has a nucleus consisting of 238 protons and neutrons, and \(^{235}U\) has a nucleus consisting of 235 protons and neutrons. Atomic number, on the other hand, represents the number of protons in the nucleus of an atom, and proton number and neutron number are not commonly used scientific terms.

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If the current is doubled, the heating power will also double, which means that the coil will generate twice as much heat per unit of time. Since the amount of water to be boiled is the same, the amount of heat needed to raise its temperature to boiling point will also be the same. However, with twice the heating power, the time required to deliver that amount of heat will be halved. Therefore, the time it will take to boil the water using the doubled current will be half of the time it took with the original current, which is 2 minutes. So the answer is 2 minutes.

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A satellite in circular motion around the earth does not have a uniform velocity. Even though its speed is constant, the direction of its velocity is constantly changing due to the centripetal force provided by the gravitational force of the earth. Therefore, it has an acceleration towards the center of the circle, which is equal in magnitude to the centripetal force acting on it.

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In a hydraulic press, the pressure exerted is constant throughout the system. The pressure exerted is given by the formula: Pressure = Force / Area The force is directly proportional to the product of the pressure and area. F ∝ P.A If F₁ is the force applied on the smaller piston of area A₁, and F₂ is the force on the larger piston of area A₂, then: F₁ / A₁ = F₂ / A₂ Rearranging the formula above to solve for F₂: F₂ = F₁ x (A₂ / A₁) Substituting the values given in the question, we get: F₂ = 40N x (200cm² / 10cm²) = 800N Therefore, the force obtained is 800N. The answer is (a) 800N.

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To calculate the magnitude of the impulse received by the body, we need to use the impulse-momentum theorem, which states that the impulse applied to a body is equal to the change in momentum of the body. The momentum of an object is defined as the product of its mass and velocity, i.e., P = mv, where P is momentum, m is mass, and v is velocity. The change in momentum (ΔP) of the body can be calculated as the difference between the final momentum (P_f) and the initial momentum (P_i), i.e., ΔP = P_f - P_i. In this case, the initial momentum of the body is given by P_i = mv = 5 kg x 30 m/s = 150 kg m/s (due east), and the final momentum is given by P_f = mv = 5 kg x 50 m/s = 250 kg m/s (due east). Therefore, the change in momentum (ΔP) of the body is: ΔP = P_f - P_i = 250 kg m/s - 150 kg m/s = 100 kg m/s (due east). The magnitude of the impulse (J) received by the body is equal to the change in momentum (ΔP), i.e., J = ΔP = 100 kg m/s. Therefore, the answer is option A: 100 Ns.

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The rate at which the boat receives the waves is equal to the frequency of the waves. The distance between successive crests of the waves is 10m, which is also the wavelength of the wave. Therefore, the formula for the speed of the wave can be written as: speed = wavelength x frequency We are given the speed of the wave as 30m/s and the wavelength as 10m. Rearranging the formula above to solve for frequency gives: frequency = speed / wavelength Substituting the values we have: frequency = 30m/s / 10m = 3s^-1 Therefore, the rate at which the boat receives the waves is 3s^-1, which is option (C).

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When a conductor mounted on an insulating stand is charged and left for some time, the conductor eventually loses all its charges. This happens because the charges on the conductor attract opposite charges from the surrounding air, which neutralize the charge on the conductor. This process is called electrostatic discharge or simply discharge. As a result, the charges are dissipated, and the conductor becomes neutral again. Therefore, the correct option is "charges on the conductor are neutralized by opposite charges from the surrounding air".

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The resistance of a wire can be calculated using the formula R = \(\frac{\rho L}{A}\), where R is the resistance, \(\rho\) is the resistivity of the wire, L is the length of the wire, and A is the cross-sectional area of the wire. In this problem, we are given the resistivity of the wire and the cross-sectional area of the wire. We are also told that the wire needs to have a resistance of 4.0\(\Omega\). We can rearrange the formula to solve for L: L = \(\frac{AR}{\rho}\) Substituting the values given in the question, we have: L = \(\frac{(7.50 \times 10^{-4} cm^{2}) (4.0 \Omega)}{4.40 \times 10^{-5} \Omega cm}\) = 68.18 cm Therefore, the length of the wire required to make a 4.0\(\Omega\) resistor is 68.18 cm. The correct option is: 68.18cm.

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Sound interference is necessary to produce the phenomenon of beats. Beats are produced when two sound waves of slightly different frequencies are superimposed on each other. The interference of these sound waves causes the sound intensity to oscillate, resulting in a periodic variation of loudness known as beats. These beats can be heard as a throbbing sound. The number of beats produced per second is equal to the difference in frequency between the two sound waves. The phenomenon of beats is used in tuning musical instruments to ensure they are in tune with each other.

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The property that will have a different value if measured in space is (i) weight. Weight is the force with which an object is attracted towards the center of the earth due to gravity. In space, there is no gravity or the gravitational force is very weak compared to that on earth. Therefore, the weight of an object measured on earth will be different from the weight of the same object measured in space. On the other hand, specific heat capacity and density are intrinsic properties of a substance that do not depend on the gravitational force, so they will have the same value whether measured on earth or in space. Thus, the answer is (i) only.

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When the stone is dropped, it gains potential energy due to its position above the ground. This potential energy is converted into kinetic energy as the stone falls towards the ground. The maximum kinetic energy of the stone will occur just before it hits the ground when all its potential energy has been converted to kinetic energy. The potential energy of the stone is given by the formula P.E. = mgh, where m is the mass of the stone, g is the acceleration due to gravity and h is the height from which it is dropped. Substituting the given values into the formula, we get: P.E. = (0.5 kg)(10 ms^-2)(12 m) = 60 J Since the maximum kinetic energy is equal to the potential energy at the maximum height, the maximum kinetic energy of the stone is also 60 J. Therefore, the correct option is (d) 60.0 J.

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In an AC circuit, the current is constantly changing direction and amplitude, and we use the root mean square (rms) value to measure the effective current flowing in the circuit. The peak value is the maximum value the current can reach, and it is equal to the square root of 2 times the rms value. So, in this case, we can use the formula: Peak value = sqrt(2) x rms value Given that the ammeter records 5.5, which is the rms value, we can calculate the peak value as follows: Peak value = sqrt(2) x 5.5 Peak value = 7.77 Rounded to one decimal place, the answer is 7.8A. Therefore, option A is the correct answer.

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The characteristic of light that determines its color is wavelength. Wavelength is the distance between consecutive peaks or troughs of a wave. Different colors of light have different wavelengths, with longer wavelengths corresponding to colors like red and orange, and shorter wavelengths corresponding to colors like blue and violet. So, when light interacts with an object and some wavelengths are absorbed while others are reflected or transmitted, the color that we perceive is determined by the wavelengths that are reflected or transmitted to our eyes. Therefore, the wavelength is responsible for the color of light we see.

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The wavelength of the associated wave of a moving particle can be determined using the de Broglie equation, which relates the particle's momentum to its wavelength: λ = h / p where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. We can determine the momentum of the electron using the formula: p = m * v where p is the momentum, m is the mass, and v is the velocity. Substituting the given values, we get: p = (9.1 x 10^-31 kg) * (10^7 ms^-1) = 9.1 x 10^-24 kgms^-1 Substituting p into the de Broglie equation, we get: λ = h / p = (6.6 x 10^-34 Js) / (9.1 x 10^-24 kgms^-1) = 7.25 x 10^-11 m Therefore, the wavelength of the associated wave is 7.25 x 10^-11 m. The correct option is (c) 7.25 x 10^-11 m.

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Electric energy is measured in kilowatt-hour (kWh). A kilowatt-hour is a unit of energy equivalent to the energy used by a load of one kilowatt in one hour. This unit is commonly used by electric utility companies to measure the amount of energy consumed by households or businesses. An ampere is a unit of electric current, while a coulomb is a unit of electric charge. A kilowatt is a unit of power, which is the rate at which energy is consumed or produced. Therefore, none of these units are suitable for measuring electric energy.

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The phenomenon that causes light travelling through a small pinhole to not make a shadow with a distinct sharp edge is called diffraction. Diffraction is the bending of waves around an obstacle or through an opening. When light waves pass through a small pinhole, they bend and spread out after passing through the hole. As a result, the edges of the shadow become blurred, and a distinct sharp edge cannot be seen. This effect is also observed when sound waves pass through small openings, such as in the case of musical instruments. Therefore, the correct option is "diffraction".

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Alpha rays are not part of the electromagnetic spectrum. The electromagnetic spectrum includes all forms of electromagnetic radiation that differ in wavelength and frequency, including radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Alpha rays are actually alpha particles, which consist of two protons and two neutrons and are emitted by some types of radioactive materials. Alpha particles have a positive charge and are relatively large compared to other types of radiation, so they are not part of the electromagnetic spectrum.

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When table salt (sodium chloride) is added to ice, it lowers the melting point of the ice. This is because salt dissolves in the thin layer of water on the surface of the ice, forming a saltwater solution. The saltwater solution has a lower freezing point than pure water, so it requires a lower temperature to freeze. As a result, the ice melts at a lower temperature when salt is added, leading to a lowering of the melting point. This phenomenon is called freezing point depression.

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When an electric current flows through a straight wire, it generates a magnetic field around the wire. The direction of the magnetic field is dependent on the direction of the current flow. If the direction of the current flow is reversed, then the direction of the magnetic field will also be reversed. Therefore, the correct answer is: the magnetic field is oppositely directed.

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When an object is immersed in a fluid, it experiences an upward force called buoyant force or upthrust. This force is equal to the weight of the fluid displaced by the object. In this case, the volume of the object submerged in the fluid is \(\frac{3}{4}\) of its total volume. So, the volume of fluid displaced by the object is \(\frac{3}{4}\) x 0.046m³ = 0.0345m³ The weight of this displaced fluid can be calculated as: mass = density x volume = 980kgm^-3 x 0.0345m³ = 33.81kg weight = mass x g = 33.81kg x 10ms^-2 = 338.1N Therefore, the upthrust on the body is 338.1N. So, the correct answer is (C) 338.10N.

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