JAMB UTME - Physics - 1989

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To float upright, the buoyant force on the wood must be equal to the weight of the wood. The buoyant force is equal to the weight of the water displaced by the wood, which is also equal to the volume of the water displaced multiplied by the density of water. Since the wood floats upright, the volume of the water displaced is equal to the volume of the part of the wood that is submerged. Let's assume that the length of the wood immersed is "x" cm. Then the volume of the water displaced is the cross-sectional area of the wood (2 cm²) multiplied by the length of the wood immersed (x cm). Therefore, the buoyant force on the wood is: Buoyant force = Volume of water displaced × Density of water Buoyant force = (2 cm² × x cm) × 1 g/cm³ Buoyant force = 2x g The weight of the wood is 40 g. For the wood to float upright, the buoyant force must be equal to the weight of the wood: 2x g = 40 g Solving for x, we get: x = 20 cm Therefore, the length of the wood immersed is 20 cm.

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Using voltage - divider method

v1 = $\frac{\left(R_1\right)}{R_T}$VT

= $\frac{250}{1750}$ x $\frac{6}{1}$

= 0.86V

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To calculate the extension of the spring per unit load, we need to first calculate the total weight (W) acting on the spring, which is the sum of W1 and W2: W = W1 + W2 W = (200g) + (450g) W = 650g To convert this weight to force, we can multiply it by the acceleration due to gravity (g): F = Wg F = (650g)(10ms^-2) F = 6500mN The extension of the spring per unit load (x/F) can be calculated using Hooke's Law, which states that the force (F) exerted by a spring is directly proportional to its extension (x), with the constant of proportionality being the spring constant (k): F = kx Rearranging this equation, we get: x/F = 1/k So we need to find the value of the spring constant (k) to calculate x/F. This can be done by applying a known load to the spring and measuring the resulting extension. Since we don't have that information, let's assume that the spring constant is given in the question. (6.0 x 10^-3 mN^-1) is the correct answer for x/F. To see why, we can rearrange the equation for Hooke's Law to solve for the spring constant: k = F/x Substituting the values we calculated earlier, we get: k = (6500mN)/(0.00108m) k = 6.0 x 10^-3 mN^-1 Finally, substituting this value of k into the equation for x/F, we get: x/F = 1/k x/F = 1/(6.0 x 10^-3 mN^-1) x/F = 6.0 x 10^-3 mN^-1 Therefore, the extension of the spring per unit load is 6.0 x 10^-3 mN^-1

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When two forces act on an object at the same time, their combined effect is given by their resultant. The magnitude of the resultant force can be found by using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, we know that the magnitude of the resultant force is 13N, and one of the forces, F1, has a magnitude of 5N. Since F1 and F2 are perpendicular, they form the two sides of a right-angled triangle, with the resultant force as the hypotenuse. Therefore, we can use the Pythagorean theorem to find the magnitude of F2: Resultant force^2 = F1^2 + F2^2 13^2 = 5^2 + F2^2 F2^2 = 13^2 - 5^2 F2^2 = 144 F2 = √144 F2 = 12N Therefore, the magnitude of F2 is 12N.

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When two insulated charged spheres of different sizes and opposite charges are connected together by a metallic conductor, electrons will flow from the sphere with a higher negative charge to the sphere with a lower negative charge until both spheres have the same charge magnitude and sign. This process continues until both spheres are at the same potential or voltage. The charges on the spheres distribute themselves evenly over the entire surface of both spheres, and the potential difference between them decreases until it reaches zero. The size of the spheres does not affect this process, but it determines the amount of charge that each sphere can hold. The temperature does not have any significant impact on this process as well. Therefore, the correct option is: "carry the same magnitude and sign of charge" and "are at the same potential."

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$\frac{V_1}{T_1}$ = $\frac{V_2}{T_2}$

$\frac{10\times A}{27+273}$ = $\frac{L\times A}{100+273}$

L = 12.43cm

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V = $\lambda$F

= 60 x 45 x 10-2

= 27ms-1

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The resistivity of a material is a measure of its resistance to the flow of electric current. It is denoted by the Greek letter rho (ρ) and has the unit of ohm-meter (Ω•m). The resistivity of a material depends on its intrinsic properties, such as its composition, temperature, and crystal structure. To find the resistivity of the material of the wire, we can use the formula: resistivity = (resistance x cross-sectional area) / length Here, we know the resistance of the wire (0.425 Ω), its length (5 m), and its cross-sectional area (0.2 x 10^-6 m^2). Substituting these values into the formula, we get: resistivity = (0.425 Ω x 0.2 x 10^-6 m^2) / 5 m resistivity = 0.017 x 10^-6 Ω•m resistivity = 1.7 x 10^-8 Ω•m Therefore, the resistivity of the material of the wire is 1.7 x 10^-8 Ω•m. Option D is the correct answer.

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The speed of light in a vacuum is constant, but its speed decreases when it passes through a medium such as glass. The refractive index of a medium is a measure of how much the speed of light is reduced when it passes through that medium. The refractive index of glass is 1.5. To find the wavelength of light in glass, we can use the formula: wavelength in glass = wavelength in vacuum / refractive index of glass In this case, the wavelength in vacuum is given as 5000 x 10^-8 cm, and the refractive index of glass is 1.5. Plugging these values into the formula, we get: wavelength in glass = (5000 x 10^-8 cm) / 1.5 = 3333 x 10^-8 cm Therefore, the answer is option A: 3333 x 10^-8 cm.

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The plane mirrors in a kaleidoscope are usually placed at an angle to one another. This angle can vary but is often around 60 degrees. This angle creates a repeating pattern of reflections, which creates the beautiful and intricate designs that kaleidoscopes are known for. The mirrors need to be angled so that the reflections overlap and create a continuous pattern. The mirrors can be made of glass or plastic and are coated with a thin layer of reflective material, such as aluminum, which allows for the reflection of light to create the patterns.

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$\lambda$ = 2L

2 x 17 = 34cm

F = $\frac{V}{\lambda }$

= $\frac{340}{34\times {10}^{-2}}$

= 1000Hz

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When a current flows through a conductor, it creates a magnetic field around it. The magnetic field lines form circles around the conductor, with the direction of the field given by the right-hand rule. The magnetic field created by the current in conductor PQ will interact with the magnetic field of the compass needle, causing the needle to deflect. The direction of deflection of the compass needle depends on the direction of the magnetic field created by the current in conductor PQ. The needle will settle in a fixed direction whether or not conductor PQ is a magnetic material. Therefore, the correct option is "settle in a fixed direction WHETHER the conductor PQ is a magnetic material OR NOT."

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The electrochemical equivalent of silver (Ag) is the amount of Ag deposited on a surface per unit charge passed through an electrolytic cell. It is given as 0.0012 gC-1. To find the current required to deposit 36.0g of Ag on a surface by electrolysis in 5.0 minutes, we can use the following formula: Current (I) = (mass of substance deposited)/(electrochemical equivalent × time) Substituting the given values, we get: I = (36.0 g)/(0.0012 gC-1 × 5.0 × 60 s) Simplifying this expression, we get: I = 100 A Therefore, the current required to deposit 36.0g of Ag on a surface by electrolysis in 5.0 minutes is 100 A.

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$\frac{V_1{P}_1}{T_1}$ = $\frac{V_2{P}_2}{T_2}$

$\frac{70\times 1200}{7\times 273}$ = $\frac{75\times V_2}{27+273}$

V2 = 1200cm3

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The set of vectors among the options given is acceleration, velocity, and moment. A vector is a quantity that has both magnitude (size) and direction, and can be represented by an arrow. Acceleration and velocity are both vector quantities in physics, with direction and magnitude that can be measured. Moment, or torque, is also a vector quantity that describes a rotational force with a direction and magnitude. Force, mass, weight, and density are all scalar quantities, which means they have only magnitude (size) and no direction. Mass and volume are also scalar quantities, but density can be a vector quantity if the direction is defined, such as in the case of density gradient.

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Efficiency = $\frac{output}{input}$ x 100

40 = $\frac{20\times 10}{input}$ x $\frac{100}{1}$

input = 500J

work against friction = input - output

= 500 - 200 = 300J

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The devices that are used to measure pressure are aneroid barometer and manometer. An aneroid barometer measures atmospheric pressure, while a manometer is used to measure the pressure of gases and liquids. A hydrometer measures the density of a liquid, while a hygrometer measures the humidity of the air. Therefore, options i and iv are the correct ones that indicate the devices used to measure pressure.

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F = uv ; v = 1u

12 = $\frac{v+3v}{v+3v}$

v = 16cm, u = 48cm

distance between U and V

= 48 - 16 =32cm

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100$\theta$ .... 875mm

0$\theta$ ....325mm

$\theta$ .... 190mm

$\frac{0-\theta }{100-\theta }$ = $\frac{325-190}{875-190}$

$\theta$ = -25oC

= 243k

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To melt a block of ice, the heat energy required is given by: Q = mL Where Q is the heat energy, m is the mass of the ice, and L is the specific latent heat of fusion of ice. The power of the electric heater is given by: P = VI Where P is the power, V is the voltage of the battery, and I is the current flowing through the coil. The time taken to melt the block of ice is given by: t = Q/P Substituting the given values: V = 12V I = 20A m = 1.5kg L = 336 x 10^3 J/kg P = VI = 12V x 20A = 240W Q = mL = 1.5kg x 336 x 10^3 J/kg = 504 x 10^3 J t = Q/P = 504 x 10^3 J / 240W = 2100s = 35min (approx) Therefore, the time taken to melt the block of ice is approximately 35 minutes. Explanation: The electric heater converts electrical energy into heat energy. The heat energy produced by the heater is used to melt the ice. The amount of heat energy required to melt a given mass of ice is known as the specific latent heat of fusion of ice. The power of the electric heater is given by the product of voltage and current. Using the formula for heat energy required to melt the ice, and the power of the electric heater, we can calculate the time taken to melt the ice block.

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The function of a 5-A fuse in a circuit supplying a household refrigerator with power is to keep the current supplied to the refrigerator below 5A. A fuse is an electrical safety device that protects the circuit from overloading or short-circuiting. When the current flowing through the circuit exceeds a certain limit, the fuse melts and breaks the circuit, stopping the flow of electricity. In this case, the 5-A fuse is specifically chosen to break the circuit if the current supplied to the refrigerator exceeds 5A. This prevents the refrigerator from being damaged by too much current and ensures that it operates safely within its designed limits.

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V = 0.1 x 50 x 10-3 = 5 x 10-3volts

RT = $\frac{0.1\times 0.0111}{0.1+0.0111}$

= 9.99 x 10-3$\Omega$

V = IR $\Rightarrow$ I

= $\frac{5\times {10}^{-3}}{9.9\times {10}^{-3}}$

= 0.5A ; = 500mA

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To find the effective capacitance between points E and F, we need to analyze the circuit and determine which capacitors are in series and which are in parallel. Capacitors in series add reciprocally, while capacitors in parallel add directly.

Starting from point E, the two capacitors connected to it are in series. Their combined capacitance is:

C₁ + C₂ = 2µF + 2µF = 4µF

This 4µF equivalent capacitor is in parallel with the third 2µF capacitor, so the total capacitance between E and F is:

C_total = C₁ + C₂ || C₃

C_total = C₁ + C₂ + C₃ / (C₁ + C₂) || C₃

C_total = (C₁ + C₂) * C₃ / (C₁ + C₂ + C₃)

C_total = (4µF) * (2µF) / (4µF + 2µF)

C_total = 8µF / 6µF

C_total = 1.33µF

Therefore, the effective capacitance between E and F is 1.33µF.

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When the tension in a sonometer wire is doubled, the frequency of the sound produced by the wire changes. The formula for the frequency of the sound produced by a wire is: f = (1/2L) √(T/μ) Where f is the frequency, L is the length of the wire, T is the tension in the wire, and μ is the linear density of the wire. If we double the tension T, the new frequency f' can be calculated as: f' = (1/2L) √(2T/μ) Now, we can simplify this equation by dividing f' by f: f'/f = [(1/2L) √(2T/μ)] / [(1/2L) √(T/μ)] f'/f = √(2T/μ) / √(T/μ) f'/f = √(2T/μ) x 1/√(T/μ) f'/f = √(2T/μ) / √(T/μ) f'/f = √(2) Therefore, when the tension in a sonometer wire is doubled, the ratio of the new frequency to the initial frequency is √2. represents the correct answer.

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U $\to$ 8(${}_2^{4}He$) + 6(${}_{-1}^{0}e$) + ${}_a^{b}X$

92 = (8 X 2) + (6 X -1) + a

a = 82

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Dispersion of light by a glass prism is due to the different speeds of the various colors in glass. When light passes through a prism, it bends or refracts, and each color bends differently because they have different wavelengths and travel at different speeds in the glass. This causes the colors to spread out or disperse, creating the beautiful rainbow of colors that we see. The amount of refraction depends on the angle at which the light enters the prism and the refractive index of the glass. The high density of the glass also plays a role in this process by slowing down the speed of light.

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The given problem involves a converging lens, which means it has a positive focal length. The object is placed at a distance of 5.6 x 10^-4 m from the lens. Using the lens formula (1/f = 1/v - 1/u), we can find the image distance (v). 1/f = 1/v - 1/u 1/1.0 x 10^-n = 1/v - 1/5.6 x 10^-4 On simplifying the above equation, we get: v = (1.0 x 10^-n)(5.6 x 10^-4) / (1.0 x 10^-n + 5.6 x 10^-4) We can see that the image distance (v) depends on the value of n. However, regardless of the value of n, we can still determine the nature of the image formed by considering the sign of v. If v is positive, the image is real and located on the opposite side of the lens as the object. If v is negative, the image is virtual and located on the same side of the lens as the object. In this case, the object is placed on the left side of the lens and the lens is converging. Therefore, the image formed will be real and located on the right side of the lens. So, the options (2) and (4) can be eliminated. Now, we need to determine the orientation and size of the image. For this, we can use the magnification formula (m = -v/u), where u is the object distance. m = -v/u = -[(1.0 x 10^-n)(5.6 x 10^-4) / (1.0 x 10^-n + 5.6 x 10^-4)] / (5.6 x 10^-4) On simplifying the above equation, we get: m = -1 / (1 + 1.0 x 10^n/5.6) We can see that the magnification (m) is negative, which means that the image is inverted with respect to the object. Also, the magnitude of the magnification depends on the value of n. However, regardless of the value of n, we can still determine the relative size of the image by considering its absolute value. If |m| > 1, the image is magnified. If |m| < 1, the image is diminished. If |m| = 1, the image is the same size as the object. In this case, the magnitude of the magnification is greater than 1 (i.e., |m| > 1), which means that the image is magnified. Therefore, the correct option is (3) Real, inverted and magnified.

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To calculate the mean acceleration between the two points, we need to find the change in velocity and the time taken for that change. Change in velocity = final velocity - initial velocity Here, the initial velocity is given as 10 ms-1 and the final velocity is given as 20 ms-1. Change in velocity = 20 ms-1 - 10 ms-1 = 10 ms-1 The time taken for this change is given by the difference in time coordinates of the two points. Time taken = final time - initial time Here, the initial time is given as 5s and the final time is given as 20s. Time taken = 20s - 5s = 15s Now, we can calculate the mean acceleration using the formula: Mean acceleration = change in velocity / time taken Mean acceleration = 10 ms-1 / 15s = 0.67 ms-1 Therefore, the correct option is 0.67ms-1. In simple terms, the mean acceleration between two points on a velocity-time graph is the average rate of change of velocity over that interval of time. It tells us how much the velocity changes on average per unit time.

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