WAEC SSCE - Physics - 2000 (Objective)
Question 1 Report
Borh's theory provides evidence for the
Answer Details
Bohr's theory provides evidence for the existence of energy levels in the atom. According to Bohr's theory, electrons orbit around the nucleus in specific energy levels or shells, and each shell has a fixed energy level. When an electron jumps from a higher energy level to a lower energy level, it releases energy in the form of light. This explains the observed line spectra of elements, and supports the idea of quantized energy levels in the atom. Therefore, is correct.
Question 2 Report
When white light passes through a triangular glass prism, there is dispersion because of
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When white light passes through a triangular glass prism, it separates into its constituent colors because of the difference in speed of the components of light, a phenomenon known as dispersion. The amount of refraction depends on the wavelength of the light, so different colors are refracted differently as they pass through the prism, causing them to spread out and creating a rainbow-like spectrum of colors. This happens because the refractive index of the glass prism is different for different colors of light. The higher the refractive index of a material, the slower light travels through it. Thus, the shorter wavelength blue and violet light refract more than the longer wavelength red and orange light. This phenomenon is the basis for many optical instruments, including spectrometers and rainbows.
Question 3 Report
the factor which enables the ear to distinguish between a note played on different instruments is the
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Question 4 Report
The temperature at which the saturated vapour pressure of a liquid is equal to the external atmospheric pressure is known as its
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The temperature at which the saturated vapour pressure of a liquid becomes equal to the external atmospheric pressure is called its boiling point. At this temperature, the liquid changes its phase from liquid to gas or vapor. The boiling point of a liquid is a characteristic physical property that depends on factors such as the nature of the liquid, external atmospheric pressure, and intermolecular forces between the molecules of the liquid.
Question 5 Report
A ball bearing is gently released from rest and allowed to fall through a viscous fluid. Which of the following statements about the motion is correct?
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As the ball bearing falls through the viscous fluid, the fluid exerts a resistive force against the motion of the ball bearing. This resistive force opposes the motion of the ball bearing and increases with its speed until it becomes equal to the weight of the ball bearing. At this point, the ball bearing stops accelerating and reaches a constant speed called the terminal velocity. Therefore, the correct statement about the motion is: when terminal velocity is attained, the acceleration of the ball bearing becomes zero. Option (a) is incorrect because the acceleration of the ball bearing decreases as it approaches the terminal velocity. Option (c) is incorrect because the velocity of the ball bearing increases initially, but as it approaches terminal velocity, the increase in velocity slows down until it becomes constant. Option (d) is incorrect because there is a resultant force acting on the ball bearing before it attains terminal velocity, which is the difference between the weight of the ball bearing and the resistive force of the fluid.
Question 6 Report
An inductor of inductance 10H carries a current of 0.2A. Calculate the energy stored in the inductor
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Question 7 Report
The diagram above illustrates three forces T1, T2 and 100N in equilibrium. Determine the magnitude of T1
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Question 8 Report
A bus travelling at 15ms-1 accelerates uniformly at 4ms-2, what is the distance covered in 10s?
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The initial velocity of the bus, u = 15m/s, the acceleration, a = 4m/s2, and the time, t = 10s. We can use the formula: distance = ut + (1/2)at2 Substituting the values given: distance = (15m/s)(10s) + (1/2)(4m/s2)(10s)2 distance = 150m + 200m distance = 350m Therefore, the distance covered in 10 seconds is 350m. Answer is the correct answer.
Question 9 Report
The region around a magnet in which the magnetic influence is experienced is called
Answer Details
The correct answer is "magnetic field." A magnetic field is the region around a magnet or a moving electric charge where the magnetic influence or force can be felt. It is a vector field, meaning it has both magnitude and direction, and is measured in units of tesla (T) or gauss (G). In the case of a magnet, the magnetic field is strongest at the poles and weaker as you move away from them. Magnetic fields are used in many everyday applications, such as in speakers, electric motors, and MRI machines.
Question 10 Report
An object is situated within the Earth's gravitational field. Which of the following factor does not affect the acceleration of free fall g?
Answer Details
The factor that does not affect the acceleration of free fall, g, is the mass of the object. According to Newton's law of gravitation, the acceleration of free fall is dependent on the mass of the Earth and the distance between the center of the Earth and the object. Therefore, the distance of the object from the center of the Earth, the latitude of the Earth on which the object is situated, and the rotation of the Earth will affect the acceleration of free fall, but the mass of the object will not. This means that objects with different masses will experience the same acceleration of free fall when dropped from the same height, ignoring air resistance.
Question 11 Report
calculate the inductance of an inductor whose reactance is one ohm at 50 Hz.
Question 12 Report
The resultant of two forces acting on an object is maximum when the angle between them is?
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Question 13 Report
A turning fork of frequency 600Hz is sounded over a closed resonance tube. If the first and second resonant positions are 0.130m and 0.413m respectively, calculate the speed of sound in air
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Question 14 Report
Using the force displacement diagram shown above. Calculate the work done
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The work done is equal to the area under the force-displacement graph. The graph shows a rectangle with base 5m and height 400N, which represents the work done to displace an object by 5m against a constant force of 400N. Therefore, the work done is: Work done = Base × Height = 5m × 400N = 2000J Hence, the answer is 2000J.
Question 15 Report
In which of the following transitions is the largest quantum of energy liberated by an hydrogen atom when the electron changes energy levels? [n is the quantum number]
Question 16 Report
The bob of a simple pendulum takes 0.25s to swing from its equilibrium position to one extreme end. Calculate its period
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Question 17 Report
An inelastic collision takes place between ball of known masses, just before the collision one of the ball is moving with a known velocity while the other is stationary. Which of the following physical quantities can be determined from the information given?
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Question 18 Report
A material of mass 1.0 x 10-2kg undergoes a fission process which decreases its mass by 0.02 percent. Calculate the amount of energy released in the process. (c = 3.0 x 108ms-1)
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The question involves calculating the amount of energy released during a fission process, given the initial mass and the percentage decrease in mass. The formula for calculating energy released during fission is E = Δmc^2, where Δm is the decrease in mass, c is the speed of light, and E is the energy released. In this case, the mass decreased by 0.02 percent, which means Δm = 0.02/100 * 1.0 x 10^-2 kg = 2 x 10^-6 kg. Plugging this into the formula along with the speed of light (c = 3.0 x 10^8 m/s), we get: E = (2 x 10^-6 kg) x (3.0 x 10^8 m/s)^2 E = 1.8 x 10^10 J Therefore, the amount of energy released in the fission process is 1.8 x 10^10 J, which is option D.
Question 19 Report
loudness increases as a vibrating tuning fork is brought nearer the end of a pipe containing air column due to
Answer Details
The correct answer is "resonance". When a vibrating tuning fork is brought near the end of a pipe containing an air column, the frequency of the sound produced by the tuning fork matches the natural frequency of the air column in the pipe. This causes the air column to vibrate with a large amplitude, producing a louder sound. This phenomenon is known as resonance. As the tuning fork is brought closer to the end of the pipe, the resonance effect becomes stronger, causing the sound to become louder. This effect is commonly used in musical instruments such as flutes and organs to produce a desired tone or pitch.
Question 20 Report
In the diagram given, the current passing through the 6\(\Omega\) resistor is 1.5A. Calculate the terminal p.d. of the battery in the diagram
Answer Details
To solve this problem, we need to use Kirchhoff's voltage law (KVL) which states that the sum of the potential differences around any closed loop in a circuit is zero. Starting from the positive terminal of the battery and moving clockwise around the circuit, we encounter a potential drop across the 6Ω resistor and a potential rise across the battery. Using Ohm's law, we can calculate the potential drop across the 6Ω resistor as: V = IR = 1.5A × 6Ω = 9V This means that the potential difference across the battery is: V_battery = V_6Ω + V_rise = 9V + V_rise We don't know the potential rise yet, but we can use KVL to find it. Moving clockwise around the circuit, we encounter a potential rise across the battery, a potential drop across the 4Ω resistor, and another potential drop across the 2Ω resistor. Using Ohm's law and KVL, we can write: V_rise - I × R_4Ω - I × R_2Ω = 0 where I is the current passing through the 6Ω resistor, which is also the current passing through the entire circuit. Substituting the given values, we get: V_rise - 1.5A × 4Ω - 1.5A × 2Ω = 0 V_rise = 1.5A × 6Ω = 9V Therefore, the potential difference across the battery is: V_battery = V_6Ω + V_rise = 9V + 9V = 18V So the terminal potential difference of the battery in the circuit is 18V. Therefore, the correct option is 10.80V.
Question 21 Report
A nuclide \(^{202}_{84} Y\) emits in succession an \(\alpha-particle\) and a \(\beta-particle\). The atomic number of the resulting nuclide is
Answer Details
The nuclide \(^{202}_{84} Y\) emits an \(\alpha-particle\) which consists of two protons and two neutrons, leading to a decrease in the atomic number by 2 and mass number by 4. Therefore, the resulting nuclide is \(^{198}_{82} Pb\). This nuclide then emits a \(\beta-particle\) which is an electron emitted from the nucleus, leading to an increase in the atomic number by 1 and no change in the mass number. Therefore, the atomic number of the resulting nuclide is 83. So, the answer is (b) 83.
Question 22 Report
A simple microscope forms an image 10cm from an eye close to the lens. If the object is 6cm from the eye, calculate the focal length of the lens
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Question 23 Report
The driver of a car moving with uniform speed of 40ms-1 observes a truck approaching from the opposite direction with a speed of 20ms-1. Calculate the speed of the car relative to that of the truck
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The relative speed of the car with respect to the truck is the difference between their speeds. Since the truck is moving in the opposite direction, its speed is taken as negative. Thus: Relative speed = speed of car - speed of truck = 40ms^-1 - (-20ms^-1) = 40ms^-1 + 20ms^-1 = 60ms^-1 Therefore, the speed of the car relative to that of the truck is 60ms-1.
Question 24 Report
An immersion heater is rated 120W. How long does it take the heater to raise the temperature of 1.2kg of water by 15oC. (Assuming heat lost to the surrounding is negligible. Specific heat capacity of water = 4200 Jkg-1K-1C)
Answer Details
We can use the formula: Q = mcΔT where Q is the amount of heat required to raise the temperature of the water, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature. First, let's calculate Q: Q = (1.2 kg) x (4200 Jkg^-1K^-1) x (15°C) = 75600 J This means we need to supply the water with 75600 J of heat in order to raise its temperature by 15°C. Now, let's use the formula: P = Q/t where P is the power of the immersion heater (in watts), t is the time taken (in seconds), and Q is the amount of heat supplied to the water. Converting 120W to J/s, we have: P = 120W = 120 J/s Plugging in the values for P and Q, we get: 120 J/s = 75600 J/t Solving for t, we get: t = 75600 J / 120 J/s = 630 s Converting to minutes, we get: t = 630 s / 60 s/min = 10.5 min Therefore, it would take 10.5 minutes for the immersion heater to raise the temperature of 1.2 kg of water by 15°C. Answer: 10.5 minutes
Question 25 Report
A proton of wavelength \(\lambda_o\) is emitted when an electron in an atom makes a transition from a level of energy 2E. If the electron transits from \(\frac{4}{3}E_k\) to E level, determine the wavelength of the photon that would be emitted
Answer Details
The energy of a photon 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 photon. When an electron transitions from a higher energy level to a lower energy level, the energy difference is released as a photon. Therefore, the energy of the emitted photon is equal to the difference in energy between the two levels. In this case, the electron transitions from \(\frac{4}{3}E_k\) to E level, which means the energy of the emitted photon is given by: E = (4/3)Ek - E Now, using the formula E = hc/λ, we can find the wavelength of the photon: λ = hc/E Substituting the expression for E: λ = hc/[(4/3)Ek - E] We know that the wavelength of the proton emitted by the electron transition from 2E to E is given by λ0. Therefore, we can write: 2E = hc/λ0 Rearranging for λ0: λ0 = hc/2E Substituting this expression for 2E in the formula for the energy of the emitted photon, we get: λ = hc/[(4/3)(hc/2λ0) - (hc/2λ0)] Simplifying: λ = 3λ0/4 Therefore, the wavelength of the photon that would be emitted is 3/4 of the wavelength of the proton emitted when the electron transitions from 2E to E. Answer: \(\frac{3}{4}\)\(\lambda_o\)
Question 26 Report
A wave has an amplitude equal to 4.0m, angular speed \(\frac{1}{3} \pi\) rads-1 and phase angle \(\frac{2}{3} \pi\) rad. The displacement y of the wave particle is given as
Question 27 Report
The diagram shows the variation of volume V of a glass with temperature at the point X is
Answer Details
The correct answer is -273oC. The diagram shows the variation of volume V of a glass with temperature. We can see that as the temperature approaches -273oC, the volume of the glass decreases rapidly. This is because at -273oC, all molecular motion ceases and the glass has zero volume, which is also known as absolute zero. Therefore, point X on the graph represents -273oC.
Question 28 Report
A device used to prevent wearing away of the make and-brake contacts of an induction coil is called a\an
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The device used to prevent wearing away of the make and-break contacts of an induction coil is called a capacitor. A capacitor is an electrical component that stores energy in an electric field. It consists of two conductive plates separated by an insulating material called a dielectric. In the context of an induction coil, a capacitor is used to reduce the arcing that occurs at the make and-break contacts. This is because when the contacts are separated, the voltage across them rises rapidly, and without a capacitor, this can cause arcing and damage to the contacts. The capacitor absorbs this voltage, preventing arcing and extending the life of the contacts.
Question 29 Report
If a bar magnet is accidentally broken into three pieces as shown in the diagram above, the polarities of P and Q respectively are
Answer Details
When a bar magnet is broken, each piece of the magnet will become an independent magnet with its own north (N) and south (S) pole. To determine the polarities of P and Q, we can use the fact that opposite poles of a magnet attract each other, while like poles repel each other. Looking at the diagram, we can see that P is attracted to the south pole of the larger piece of the magnet, indicating that P must have a north pole. Similarly, Q is attracted to the north pole of the larger piece of the magnet, indicating that Q must have a south pole. Therefore, the correct answer is (B) N and S.
Question 30 Report
In the diagram above, the current passing through the 6\(\Omega\) resistor is 1.5A. Calculate the current in the 30\(\Omega\) resistor
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Question 31 Report
A uniform metre rule of mass 90g is provided at the 40cm mark. If the rule is in equilibrium with an unknown mass m placed at the 10cm mark and a 72g mass at the 70cm mark, determine m
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Question 32 Report
The mass of water vapour in a given volume of air is 0.05g at 20oC, while the mass of water vapour required to saturate it at the same temperature is 0.15g. Calculate the relative humidity of the air
Answer Details
The relative humidity is the ratio of the actual amount of water vapour present in the air to the maximum amount of water vapour that can be present in the air at a given temperature expressed as a percentage. In this question, the actual amount of water vapour present in the air is given as 0.05g and the mass of water vapour required to saturate it at the same temperature is given as 0.15g. So, the relative humidity can be calculated as: Relative humidity = (actual amount of water vapour/maximum amount of water vapour) x 100% Maximum amount of water vapour is the mass of water vapour required to saturate the air, which is given as 0.15g. Therefore, Relative humidity = (0.05/0.15) x 100% = 33.33% Hence, the relative humidity of the air is 33.33%. Option (c) is the correct answer.
Question 34 Report
The period of oscillation pf a particle executing simple harmonic motion is 4\(\pi\) seconds. If the amplitude of oscillation is 3.0m. Calculate its period
Question 35 Report
The duality of matter implies that matter
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The duality of matter implies that matter has both wave and particle properties. In physics, duality refers to the idea that matter can exhibit characteristics of both waves and particles. This concept is best illustrated by the famous double-slit experiment, which showed that particles, such as electrons, can exhibit wave-like behavior, such as diffraction and interference. Conversely, waves, such as light, can exhibit particle-like behavior, such as the photoelectric effect. The duality of matter is an important concept in quantum mechanics and helps explain the behavior of matter on both a microscopic and macroscopic scale.
Question 36 Report
The volume and pressure of a given mass of gas at 27oC are 76cm3 and 80cm of mercury respectively. Calculate the volume at s.t.p
Answer Details
To solve the problem, we need to use the combined gas law, which relates the pressure, volume, and temperature of a gas. The combined gas law states that: P1V1/T1 = P2V2/T2 where P1, V1, and T1 are the initial pressure, volume, and temperature, respectively, and P2, V2, and T2 are the final pressure, volume, and temperature, respectively. We are given the initial pressure, volume, and temperature of the gas as P1 = 80 cmHg, V1 = 76 cm^3, and T1 = 27°C. We want to find the volume of the gas at STP, which is a temperature of 0°C and a pressure of 1 atm (or 760 mmHg). To use the combined gas law, we need to convert the initial temperature to kelvin (K), since temperature must be in kelvin in this equation. We do this by adding 273 to the initial temperature: T1 = 27°C + 273 = 300 K We also need to convert the initial pressure from cmHg to atm, using the conversion factor: 1 atm = 760 mmHg = 101.325 kPa = 76 cmHg So, the initial pressure in atm is: P1 = 80 cmHg × (1 atm/76 cmHg) = 1.05 atm Now we can plug in the values into the combined gas law, with the final pressure P2 = 1 atm and the final temperature T2 = 0°C + 273 = 273 K: P1V1/T1 = P2V2/T2 (1.05 atm)(76 cm^3)/(300 K) = (1 atm)(V2)/(273 K) Solving for V2 gives: V2 = (1.05 atm)(76 cm^3)(273 K)/(300 K) = 72.8 cm^3 Therefore, the volume of the gas at STP is 72.8 cm^3, which is.
Question 37 Report
In the diagram above, an incident ray AY makes an angle of 30o with the normal XY. If the mirror is rotated anticlockwise about Y through an angle of 20o, while AY is fixed, what angle will the reflected ray now make with the incident ray?
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Question 38 Report
A concave mirror can be used to produce a parallel beam of light if a lighted bulb is placed
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A concave mirror is a mirror that curves inward, like the inside of a spoon. The property of a concave mirror that allows it to produce a parallel beam of light is its ability to reflect incoming light rays in such a way that they all converge to a single point called the focal point. When an object is placed between the focus and the pole of a concave mirror, a virtual, upright, and magnified image is formed behind the mirror. However, if a lighted bulb is placed at the focus of a concave mirror, the incoming light rays are reflected parallel to the principal axis of the mirror. Therefore, the correct answer is "at its focus."
Question 39 Report
A periodic pulse travels a distance of 20.0m in 1.00s. If its frequency is 2.0 x 103Hz. Calculate the wavelength.
Answer Details
The speed of a wave is given by the product of its wavelength and frequency. Therefore, we can use the formula: v = λf where v is the speed of the wave, λ is the wavelength, and f is the frequency. In this problem, we are given the frequency of the wave as 2.0 x 10^3 Hz and the distance it travels in 1.00 second as 20.0 m. We can calculate the speed of the wave as: v = distance/time = 20.0 m/1.00 s = 20.0 m/s Now, we can rearrange the formula to solve for the wavelength: λ = v/f = 20.0 m/s / 2.0 x 10^3 Hz = 1.0 x 10^-2 m Therefore, the wavelength of the wave is 1.0 x 10^-2 m. Answer: 1.0 x 10^-2 m
Question 40 Report
A piece of metal of mass 50g is cooled from 80oC to 20oC. Calculate the amount of heat lost. (specific heat capacity of the material of metal = 450Jkg-1K-1)
Answer Details
The amount of heat lost by an object is given by the formula: Q = mcΔT where Q is the amount of heat lost or gained, m is the mass of the object, c is the specific heat capacity of the material, and ΔT is the change in temperature. In this question, the mass of the metal is given as 50g, which is 0.05kg. The specific heat capacity of the material of the metal is given as 450Jkg-1K-1. The change in temperature is 80oC - 20oC = 60oC. Substituting the given values into the formula: Q = (0.05kg)(450Jkg-1K-1)(60K) Q = 1.35 x 103J Therefore, the amount of heat lost by the piece of metal is 1.35 x 103J. Option (d) is the correct answer.
Question 41 Report
The apparent weight of a body wholly immersed in water is 32N and its weight in air is 96N. Calculate the volume of the body. (Density of water = 1000kgm-3, g = 10ms-3)
Answer Details
When a body is immersed in water, it experiences an upthrust force, which reduces its weight. According to Archimedes' principle, this upthrust force is equal to the weight of the water displaced by the body. Therefore, we can use the given data to find the volume of the body as follows: Weight of body in air = 96N Apparent weight of body in water = 32N Upthrust force = Weight of water displaced = Weight of body in air - Apparent weight of body in water Upthrust force = 96N - 32N = 64N Now, we can use the formula for upthrust force to find the volume of the body: Upthrust force = Volume of body x Density of water x g 64N = Volume of body x 1000kgm-3 x 10ms-2 Volume of body = 64N / (1000kgm-3 x 10ms-2) = 6.4 x 10-3m3 Therefore, the volume of the body is 6.4 x 10-3m3.
Question 42 Report
An iron rod is moved from the earth to the moon. Which of the following properties of the rod would remain unchanged? i. mass ii. weight iii. relative density
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Question 43 Report
The cubic expansivity of mercury is 1.8 x 10-4K-1 and the linear expansivity of glass 8.0 x 10-6K-1, calculate the apparent expansivity of mercury in a glass container
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Question 44 Report
In a nuclear reactor, electricity can be generated through the following processes. Arrange the processes in the correct order. i. The steam is used to drive turbines. ii. The heat energy released is removed by passing water through the reactor. iii. The turbines in turn generate electricity. iv. The water then passes through some form of heat exchanger to produce steam
Answer Details
The correct order of processes for generating electricity in a nuclear reactor is: ii. The heat energy released is removed by passing water through the reactor. iv. The water then passes through some form of heat exchanger to produce steam. i. The steam is used to drive turbines. iii. The turbines in turn generate electricity. This is because in a nuclear reactor, the heat energy is produced by the nuclear fission reactions occurring within the fuel rods. This heat energy is then used to heat up water, which is circulated through the reactor core to remove the heat energy. This is the second process (ii) mentioned in the options. The hot water then passes through a heat exchanger, which is the fourth process (iv) mentioned in the options. The heat exchanger uses the hot water to produce steam, which drives the turbines. This is the first process (i) mentioned in the options. Finally, the turbines generate electricity by rotating a generator, which is the third process (iii) mentioned in the options. Therefore, the correct order of processes is ii, iv, i, and iii.
Question 45 Report
The nucleon number and the proton number of a neutral atom of an element are 23 and 11 respectively. How many neutrons are present in the atom?
Answer Details
The nucleon number of an atom is the sum of the number of protons and the number of neutrons in the nucleus of the atom. Therefore, the number of neutrons in the atom can be calculated by subtracting the number of protons (which is given as 11) from the nucleon number (which is given as 23). So, Number of neutrons = Nucleon number - Proton number = 23 - 11 = 12 Therefore, there are 12 neutrons present in the atom. The correct answer is (ii) 12.
Question 46 Report
The capacitance of a parallel-plate capacitor is increased by making the area of the plates
Answer Details
The capacitance of a parallel-plate capacitor is directly proportional to the area of the plates and inversely proportional to the distance between the plates. This means that by increasing the area of the plates, the capacitance of the capacitor will increase. This can be seen from the capacitance equation, which is given as C = εA/d, where C is the capacitance, ε is the permittivity of the dielectric material between the plates, A is the area of the plates, and d is the distance between the plates. Thus, the larger the area of the plates, the larger the capacitance of the capacitor. Therefore, the correct option is: large and their separation small.
Question 47 Report
Absorption line spectra exhibited by atoms is a result of
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Absorption line spectra exhibited by atoms is a result of the transition of an electron from a higher to a lower energy level. When energy is absorbed by an atom, an electron moves from a lower energy level to a higher one. Conversely, when an electron moves from a higher energy level to a lower one, energy is emitted in the form of electromagnetic radiation. This radiation is observed as a spectrum of colored lines with specific wavelengths that correspond to the specific energy levels involved in the transition. The spectrum produced is unique for each atom, providing a way to identify the atoms present in a sample. Therefore, the correct option is (d) transition of an electron from a higher to a lower energy level.
Question 48 Report
Two bodies P and Q, are in thermal equilibrium, which of the following statements about the bodies is correct?
Answer Details
When two objects are in thermal equilibrium, it means that they are at the same temperature. This means that the heat energy flows between them at equal rates, and as a result, the temperatures of the two objects will remain constant over time. Therefore, the correct statement about the bodies is that P and Q are at the same temperature. The other options may or may not be true, depending on the specific situation, but they are not necessarily related to the fact that the bodies are in thermal equilibrium.
Question 49 Report
A machine of efficiency 8% is used to raise a body of mass 75kg through a vertical height of 3m in 30s. Calculate the power input. (g = 10ms-2)
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Efficiency of a machine is defined as the ratio of output work to the input work. Mathematically, efficiency = (output work / input work) x 100%. In this question, the machine has an efficiency of 8%, which means that only 8% of the input work is converted into useful work. The rest is lost as heat or other forms of energy. Therefore, the output work of the machine is 8% of the input work. The machine is used to raise a body of mass 75kg through a vertical height of 3m in 30s. The work done by the machine is equal to the gravitational potential energy gained by the body. The gravitational potential energy gained by an object of mass m raised through a height h is given by the formula mgh, where g is the acceleration due to gravity. Therefore, the work done by the machine is W = mgh = 75 x 10 x 3 = 2250 J. We are asked to calculate the power input, which is the rate at which work is done by the machine. Power is given by the formula power = work done / time taken. Substituting the values, we get power = 2250 / 30 = 75 W. However, this is the output power of the machine. We need to calculate the input power, which is the power required to produce this output power, taking into account the efficiency of the machine. The input power is given by the formula input power = output power / efficiency. Substituting the values, we get input power = 75 / 0.08 = 937.5 W. Therefore, the power input is approximately 937.5 W, which is closest to option D: 93.8 W.
Question 50 Report
A uniform cylindrical hydrometer of mass 20g and cross sectional area 0.54cm2 floats upright in a liquid. If 25cm of its length is submerged, calculate the relative density of the liquid. (Density of water = 1 gcm-3)
Answer Details
When a hydrometer floats in a liquid, it displaces an amount of liquid equal to its own volume, and the weight of the liquid displaced acts as an upthrust to balance the weight of the hydrometer. If the hydrometer floats with 25 cm of its length submerged, then the volume of liquid displaced by the hydrometer is equal to the volume of the submerged part of the hydrometer, which is given by the formula V = Al, where A is the cross-sectional area of the hydrometer and l is the length submerged. So, the volume of liquid displaced is V = 0.54 cm2 x 25 cm = 13.5 cm3. The weight of the liquid displaced is equal to the weight of the hydrometer, which is given by the formula W = mg, where m is the mass of the hydrometer and g is the acceleration due to gravity. So, W = 0.02 kg x 9.81 m/s2 = 0.1962 N. The relative density of the liquid is given by the formula ρliquid/ρwater = Fupthrust/W, where Fupthrust is the upthrust on the hydrometer due to the liquid. The upthrust is equal to the weight of the liquid displaced, which we have already calculated to be 0.1962 N. So, ρliquid/ρwater = 0.1962 N / (0.54 cm2 x 25 cm x 9.81 m/s2 x 1 g/cm3) = 1.48 Therefore, the relative density of the liquid is 1.48. Answer (b) 1.48.
Question 51 Report
The half life of a radioactive substance is 14 days. If 48g of this substance is stored, after how many days will 1.5g of the original substance remain?
Answer Details
The half-life of a radioactive substance is the time taken for the substance to reduce to half of its original quantity. In this case, the half-life of the substance is 14 days, which means that after 14 days, half of the substance would have decayed. Let's calculate how many half-lives are needed for 48g to reduce to 1.5g: 48g → 24g (1 half-life) 24g → 12g (2 half-lives) 12g → 6g (3 half-lives) 6g → 3g (4 half-lives) 3g → 1.5g (5 half-lives) Therefore, it will take 5 half-lives for 48g of the substance to decay to 1.5g. The total time taken for 5 half-lives is 5 x 14 = 70 days. Therefore, after 70 days, 1.5g of the original substance will remain. Hence, the answer is 70 days.
Question 52 Report
A wooden block of mass 1.6kg rest on a rough horizontal surface, if the limiting friction force between the block and the surface is 8N. Calculate the coefficient of friction. (g = 10ms-2)
Answer Details
The coefficient of friction (μ) is the ratio of the frictional force (F) to the normal force (N) between two surfaces in contact. In this case, the normal force is equal to the weight of the block, which is given by: N = mg where m is the mass of the block and g is the acceleration due to gravity (10ms-2). N = 1.6 kg x 10 ms-2 = 16 N The limiting friction force (F) is given as 8N. Therefore, we have: F = μN Substituting the values we have obtained, we can solve for μ as follows: μ = F/N = 8N/16N = 0.5 Therefore, the coefficient of friction is 0.5. Answer: 0.5
