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Question 1 Report
An explosion occurs at an altitude of 312 m above the ground. If the air temperature is -10.00°C, how long does it take the sound to reach the ground?
[velocity of sound at 0 deg = 331 ms-1]
Question 2 Report
Question 3 Report
Three forces with magnitudes 16 N, 12 N and 21 N are shown in the diagram below. Determine the magnitude of their resultant force and angle with the x-axis
Answer Details
Question 4 Report
A 400 N box is being pushed across a level floor at a constant speed by a force P of 100 N at an angle of 30.0° to the horizontal, as shown in the the diagram below. What is the coefficient of kinetic friction between the box and the floor?
Answer Details
W = 400 N; P = 100 N; θ = 30o; μ = ?
Frictional force (Fr) = μR (where R is the normal reaction)
The forces acting along the horizontal direction are Fr and Px
∴ Pcos 30° - Fr = ma (Pcos 30° is acting in the +ve x-axis while Fr in the -ve x-axis)
⇒ 100cos 30° - μR = ma
Since the box is moving at constant speed, its acceleration is zero
⇒ 100cos 30° - μR = 0
⇒ 100cos 30o = μR ----- (i)
The forces acting in the vertical direction are W, Py and R
∴ R - Psin 30° - W = 0 (R is acting upward (+ve) while Py and W are acting downward (-ve) and they are at equilibrium)
⇒ R - 100sin 30° - 400 = 0
⇒ R = 100sin 30° + 400
⇒ R = 50 + 400 = 450 N
From equation (i)
⇒ 100cos 30° = 450μ
⇒μ=100cos30°
N = 100cos30°450
$\frac{\mathrm{}}{}$
= μ = 0.19
Question 5 Report
The diagram above illustrates the penetrating power of some types of radiation. X, Y and Z are likely
Answer Details
The penetrating power of alpha rays, beta rays, and gamma rays varies greatly. Alpha particles can be blocked by a few pieces of paper. Beta particles pass through paper but are stopped by aluminum foil. Gamma rays are the most difficult to stop and require concrete, lead, or other heavy shielding to block them.
Therefore, X = γ-ray; Y = α-particle; Z = β-particle
Question 6 Report
Which of the following liquids has the highest surface tension?
Answer Details
Surface tension is a property of liquids that arises due to the cohesive forces between the molecules at the surface. It can be thought of as the "skin" or "film" that forms on the surface of a liquid.
Considering the options given:
- Water: Water molecules have strong cohesive forces, allowing them to form hydrogen bonds with each other. As a result, water has relatively high surface tension.
- Mercury: Mercury is a metal with metallic bonding, which is much stronger than the cohesive forces in liquids. As a result, mercury has very high surface tension.
- Oil: Oils typically consist of nonpolar molecules, which have weaker cohesive forces compared to polar molecules like water. Therefore, oil generally has lower surface tension than water.
Based on this information, we can conclude that mercury has the highest surface tension among these liquids.
Question 7 Report
A travelling wave of amplitude 0.80 m has a frequency of 16 Hz and a wave speed of 20 ms-1
Calculate the wave number of the wave.
Answer Details
The wave number of a wave is defined as the number of wavelengths per unit distance. It represents the spatial frequency of the wave.
In this case, the wave has a frequency of 16 Hz, which means it completes 16 cycles or oscillations per second. Each cycle corresponds to one wavelength.
The wave speed is given as 20 m/s, which is the speed at which the wave propagates through the medium.
To calculate the wave number, we can use the formula:
Wave number (k) = 2? / wavelength (?)
First, we need to find the wavelength of the wave. We can use the formula:
Wave speed (v) = frequency (f) x wavelength (?)
Rewriting the formula, we have:
Wavelength (?) = wave speed (v) / frequency (f)
Substituting the given values, we have:
Wavelength (?) = 20 m/s / 16 Hz
Simplifying the expression, we get:
Wavelength (?) = 1.25 m
Now, we can calculate the wave number using the formula:
Wave number (k) = 2? / wavelength (?)
Substituting the value of the wavelength, we get:
Wave number (k) = 2? / 1.25 m
Simplifying the expression, we get:
Wave number (k) ? 5.03
Therefore, the wave number of the wave is approximately 5.
Question 8 Report
A lorry accelerates uniformly in a straight line with acceleration of 4ms-1 and covers a distance of 250 m in a time interval of 10 s. How far will it travel in the next 10 s?
Answer Details
Question 9 Report
The half life of a radioactive material is 12 days. Calculate the decay constant.
Answer Details
The decay constant of a radioactive material represents the probability that an atom of the material will decay in a unit of time. In this case, we are given the half-life of the material which is the time it takes for half of the radioactive atoms to decay.
The relationship between the decay constant (λ) and the half-life (T½) is given by the formula:
λ = ln(2) / T½
where ln(2) is the natural logarithm of 2.
To find the decay constant, we can plug in the given half-life value into the formula. In this case, the half-life is 12 days.
λ = ln(2) / 12
Using a calculator, we can calculate the value of ln(2) ≈ 0.6931.
λ = 0.6931 / 12 ≈ 0.05775 day^(-1)
Therefore, the decay constant for this radioactive material is approximately 0.05775 day^(-1).
The correct answer is 0.05775 day^(-1).
Question 10 Report
From the diagram above, if the potential difference across the resistor, capacitor and inductor are 60V, 120V and 30V respectively, the effective potential difference is
Answer Details
Question 11 Report
A 200 kg load is raised using a 110 m long lever as shown in the diagram above. The load is 10m from the pivot P. If the efficiency of the the lever is 80%, find the effort E required to lift the load.
[Take g = 10ms-2]
Answer Details
To find the effort E required to lift the load, we first need to understand the concept of mechanical efficiency in levers.
A lever is a simple machine that consists of a rigid beam (lever arm) that pivots around a fixed point called the fulcrum. In this case, the fulcrum is point P.
The mechanical efficiency of a lever is defined as the ratio of the output work done (load lifted) to the input work done (effort applied). Mathematically, it can be expressed as:
Efficiency = (Output Work / Input Work) * 100%
In this problem, the load is the output work and the effort is the input work.
Given: Load = 200 kg Length of lever (distance between fulcrum and load) = 10 m Efficiency = 80% Gravitational acceleration (g) = 10 m/s^2
To calculate the effort, let's first calculate the output work:
Output Work = Load * Distance lifted
The distance lifted is equal to the length of the lever arm, which is 10 m.
Output Work = 200 kg * 10 m = 2000 kg·m
Since 1 kg·m is equivalent to 10 J (1 Joule), we can convert the units:
Output Work = 2000 kg·m * 10 J/kg·m = 20000 J
Now, let's calculate the input work:
Input Work = Effort * Distance moved by the effort
The distance moved by the effort is the length of the lever arm, which is 110 m.
Input Work = Effort * 110 m
Using the formula for mechanical efficiency, we can rewrite it as:
Efficiency = (Output Work / Input Work) * 100%
Solving for the effort:
Effort = (Output Work / (Efficiency/100)) / Distance moved by the effort
Effort = (20000 J / (80/100)) / 110 m
Simplifying the equation:
Effort = (20000 J / 0.8) / 110 m
Effort = 250 J / m
Given that g = 10 m/s^2, we know that 1 N = 1 kg·m/s^2. Therefore, we can convert the units:
Effort = (250 J / m) / (1 kg·m/s^2 / 1 N)
Effort = 250 N
Therefore, the effort E required to lift the load is 250 N.
Question 12 Report
Rainbow formation is as a result of the combination of which of the following phenomena?
(i) Reflection
(ii) Dispersion
(iii) Total internal reflection
(iv) Refraction
Answer Details
As light ray enters a drop of water the light is refracted at the surface and at the end of the drop, it is totally internally reflected in which the reflected light returns to the front surface, where it again undergoes refraction as it moves from water to air. The result of this is a dispersed light of colours of different wavelengths.
Question 13 Report
The sensitivity of a thermometer is
Answer Details
The sensitivity of a thermometer refers to the smallest temperature change that it can detect or measure. In other words, it measures how fine or precise the thermometer is in detecting changes in temperature. A thermometer with high sensitivity is able to detect even small changes in temperature, while a thermometer with low sensitivity may only detect larger temperature fluctuations.
Therefore, in the given options, the statement "the smallest temperature change that can be detected or measured" accurately describes the sensitivity of a thermometer.
Question 14 Report
A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Young's modulus for the material of the wire.
[Take g = 10 ms-2]
Question 15 Report
The electrolyte used in the Nickel-Iron (NiFe) accumulator is
Answer Details
The electrolyte used in the Nickel-Iron (NiFe) accumulator is **potassium hydroxide solution**.
In a Nickel-Iron accumulator, the electrolyte is the substance that allows the flow of electric current between the electrodes. It is essential for the proper functioning of the accumulator.
Potassium hydroxide solution is the ideal electrolyte for the NiFe accumulator due to its properties. It has good electrical conductivity, which means it allows the movement of ions between the positive and negative electrodes, enabling the flow of electrons and facilitating the charging and discharging process.
In addition to good conductivity, potassium hydroxide solution also has other beneficial properties for the NiFe accumulator. It is stable, ensuring a longer lifespan for the accumulator. It is also less prone to self-discharge, meaning the accumulator can retain its charge for a longer period without significant loss.
Therefore, the electrolyte used in the Nickel-Iron (NiFe) accumulator is potassium hydroxide solution.
Question 16 Report
How much work is done against the gravitational force on a 3.0 kg object when it is carried from the ground floor to the roof of a building, a vertical climb of 240 m?
Answer Details
To calculate the work done against gravitational force, we can use the formula:
Work = Force x Distance
In this case, the force we are working against is the gravitational force. The gravitational force is the force with which the Earth pulls objects towards its center. The formula for gravitational force is:
Force = Mass x Acceleration due to gravity
The mass of the object is given as 3.0 kg. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Now, we need to find the distance the object is being carried, which is 240 m.
Plugging these values into the formulas, we have:
Force = 3.0 kg x 9.8 m/s^2 = 29.4 N
Work = 29.4 N x 240 m
Therefore, the work done against the gravitational force is equal to 29.4 N x 240 m = 7056 J = 7.1 kJ (rounded to one decimal place).
So, the correct answer is 7.2 kJ.
Question 17 Report
A parallel plate capacitor separated by an air gap is made of 0.8m2 tin plates and 20 mm apart. It is connected to 120 V battery. What is the charge on each plate?
Take εo = 8.85 * 10-12 Fm−1
Answer Details
To calculate the charge on each plate of a parallel plate capacitor, we can use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage applied. The capacitance of a parallel plate capacitor can be calculated using the formula C = εA/d, where C is the capacitance, ε is the permittivity of the medium (in this case, air), A is the area of each plate, and d is the distance between the plates. Given: Area of each plate (A) = 0.8 m^2 Distance between the plates (d) = 20 mm = 0.02 m Permittivity of air (ε) = 8.85 x 10^-12 F/m Using the formula for capacitance, we can calculate C: C = εA/d = (8.85 x 10^-12 F/m)(0.8 m^2)/(0.02 m) = 8.85 x 10^-12 F/m * 40 F = 3.54 x 10^-10 F Now, we can use the formula Q = CV to calculate the charge on each plate: Q = (3.54 x 10^-10 F)(120 V) = 4.25 x 10^-8 C = 42.5 x 10^-9 C = 42.5 nC Therefore, the charge on each plate of the parallel plate capacitor is **42.5 nC**.
Question 18 Report
Which of the following statements is correct about the angle of dip at various points on Earth?
Answer Details
The correct statement about the angle of dip at various points on Earth is: The angle of dip is zero at the equator and 90 degrees at the magnetic poles.
The angle of dip, also known as the inclination, refers to the angle between the Earth's magnetic field lines and the horizontal plane at a specific location. It tells us how much the magnetic field lines of the Earth are inclined or tilted at that point.
At the equator, the angle of dip is zero. This means that the magnetic field lines are parallel to the horizontal plane. As we move closer to the magnetic poles, the angle of dip increases. At the magnetic poles, the angle of dip is 90 degrees, indicating that the magnetic field lines are perpendicular to the horizontal plane.
The second statement that the angle of dip is greater at higher altitudes than at lower altitudes is incorrect. The angle of dip is primarily affected by the latitude or distance from the equator and the proximity to the magnetic poles, rather than the altitude. So, the angle of dip remains consistent at a specific latitude regardless of the altitude above sea level.
The third statement that the angle of dip is positive in the northern hemisphere and negative in the southern hemisphere is also incorrect. The angle of dip is positive in the northern hemisphere and negative in the southern hemisphere. This means that the magnetic field lines are inclined downwards in the northern hemisphere and upwards in the southern hemisphere.
The fourth statement that the angle of dip is constant at all points on Earth is incorrect as well. The angle of dip varies depending on the latitude and the proximity to the magnetic poles, as explained earlier. So, it is not constant across all points on Earth.
To summarize, the correct statement is that the angle of dip is zero at the equator and 90 degrees at the magnetic poles. It is important to note that the angle of dip is not affected by altitude but is primarily determined by latitude and proximity to the magnetic poles.
Question 19 Report
A charge of 4.6×10−5
$4.6\times {10}^{-}5$C is placed in an electric field of intensity 3.2×104
$3.2\times {10}^{4}$ Vm−1
. What is the force acting on the electron?
Answer Details
To calculate the force acting on the charge in an electric field, we can use the formula: F = q * E Where: F is the force acting on the charge, q is the charge of the particle, and E is the electric field intensity. In this case, the charge is given as 4.6 × 10^(-5) C and the electric field intensity is given as 3.2 × 10^4 V/m. Substituting these values into the formula: F = (4.6 × 10^(-5) C) * (3.2 × 10^4 V/m) To multiply numbers in scientific notation, we multiply the coefficients and add the exponents: F = (4.6 * 3.2) * (10^(-5 + 4)) C * V/m F = 14.72 * 10^(-1) C * V/m To simplify, we can convert the result to standard form: F = 1.472 C * V/m Therefore, the force acting on the charge is **1.472 N**.
Question 20 Report
The pinhole camera works on
Answer Details
The pinhole camera works on the principle of the rectilinear propagation of light. This principle states that light travels in straight lines. When light passes through the tiny hole in a pinhole camera, it forms an inverted image on the opposite side of the camera. The size of the image depends on the distance between the object and the pinhole.
Question 21 Report
Which of the following statements regarding the application of electrical conduction via gases is/are correct?
Electrical conduction in gas is applied in:
(i) The identification of gases
(ii) Lighting/fluorescent tubes
(iii) Photocells
(iv) Cathode ray oscilloscope/T.V. tubes
Answer Details
Electrical conduction of gas is applied in:
(i) The identification of gases
(ii) Lighting/fluorescent tubes
(iii) Advertising industry/Neon signs
(iv) Cathode ray oscilloscope/T.V. tubes
Question 22 Report
On a particular hot day, the temperature is 40°C and the partial pressure of water vapor in the air is 38.8 mmHg. What is the relative humidity?
Answer Details
To calculate the relative humidity, we need to understand the concept of saturation and how much water vapor the air can hold at a given temperature.
Saturation is the point at which the air is holding the maximum amount of water vapor it can hold at a particular temperature. Once the air reaches saturation, any additional moisture will start to condense into liquid water.
The amount of water vapor that the air can hold increases with temperature. Warmer air can hold more water vapor, while cooler air can hold less.
Now, let's calculate the relative humidity using the given information:
1. Find the saturation vapor pressure at 40°C: - The saturation vapor pressure is the maximum amount of water vapor the air can hold at a specific temperature. - At 40°C, the saturation vapor pressure is approximately 55.3 mmHg.
2. Calculate the relative humidity: - Relative humidity is the ratio of the current partial pressure of water vapor to the saturation vapor pressure, expressed as a percentage. - Relative Humidity = (Partial pressure of water vapor / Saturation vapor pressure) * 100 - In this case, the partial pressure of water vapor is 38.8 mmHg and the saturation vapor pressure at 40°C is 55.3 mmHg. - Plugging in these values into the formula, we get: Relative Humidity = (38.8 mmHg / 55.3 mmHg) * 100 = 70.2%
Therefore, the relative humidity on this particular hot day is approximately 70%.
Answer: The correct option is 70.
Question 23 Report
What is the amount of heat required to raise the temperature of a 0.02 kg of ice cube from −10oC to 10oC ?
[specific latent heat of fusion of ice = 3.34 x 105 Jkg−1, Specific heat capacity of water = 4200 Jkg−1 k−1
Specific heat capacity of ice = 2100 Jkg−1k−1
Question 24 Report
A missile is launched with a speed of 75 ms-1 at an angle of 22° above the surface of a warship. Find the horizontal range achieved by the missile. Ignore the effects of air resistance.
[Take g = 10 ms-1]
Question 25 Report
Which of the following is/are not true about the heat capacity of a substance?
(i) It is an intensive property
(ii) Its S.I unit is jK−1
(iii) It is an extensive property
(iv) Its S.I unit is jkg−1
Answer Details
The correct answer is (ii) and (iii) only. The heat capacity of a substance is a measure of how much heat energy is required to raise the temperature of the substance by a certain amount. It is an important property in thermodynamics. (i) It is not true that heat capacity is an intensive property. Intensive properties do not depend on the size or amount of the substance. For example, density and temperature are intensive properties. However, heat capacity does depend on the size or amount of the substance. The heat capacity of a substance increases with its mass or amount. Therefore, statement (i) is false. (ii) It is true that the SI unit of heat capacity is joules per kelvin (J/K). Heat capacity is defined as the amount of heat energy (in joules) required to raise the temperature of a substance by 1 degree kelvin. Therefore, statement (ii) is true. (iii) It is not true that heat capacity is an extensive property. Extensive properties depend on the size or amount of the substance. Examples of extensive properties include mass and volume. However, heat capacity is an intensive property as explained earlier. Therefore, statement (iii) is false. (iv) It is true that the SI unit of heat capacity is joules per kilogram per kelvin (J/(kg·K)). This unit is commonly used for specific heat capacity, which is the heat capacity per unit mass. Therefore, statement (iv) is true. In summary, the correct statement is that (ii) and (iii) are not true about the heat capacity of a substance.
Question 26 Report
The number of holes in an intrinsic semiconductor
Answer Details
The number of holes in an intrinsic semiconductor is equal to the number of free electrons.
In an intrinsic semiconductor, the valence band is completely filled with electrons. However, due to thermal energy, some of these electrons can gain enough energy to jump to the conduction band, leaving behind holes in the valence band.
For every electron that moves to the conduction band, a hole is created in the valence band. Since the number of electrons and holes is equal, the number of holes in an intrinsic semiconductor is equal to the number of free electrons.
Therefore, the correct option is: is equal to the number of free electrons.
Question 27 Report
Which process is responsible for production of energy in stars?
Answer Details
The process responsible for the production of energy in stars is nuclear fusion.
Nuclear fusion is the process where two or more atomic nuclei come together to form a heavier nucleus. In stars, the fusion of hydrogen nuclei (protons) into helium nuclei is the main source of energy.
Here's how it works:
This ongoing fusion process in stars is called stellar nucleosynthesis. It occurs throughout the star's lifetime until the available hydrogen in the core is depleted. At this point, depending on the star's mass, different fusion reactions may take place, leading to the production of heavier elements.
In summary, nuclear fusion, the fusion of hydrogen nuclei into helium nuclei, is the process responsible for the production of energy in stars.
Question 28 Report
Which of the following materials is a good insulator?
Answer Details
A good insulator is a material that does not easily allow heat or electricity to pass through it. It acts as a barrier, preventing the flow of heat or electricity. Out of the given options, rubber is a good insulator.
Rubber is made up of long chains of molecules that are closely packed together. These chains do not allow the easy movement of heat or electricity. This means that when heat or electricity tries to pass through rubber, it encounters resistance, making it difficult for it to flow.
In contrast, materials like silver, water, and copper are good conductors rather than insulators.
Silver is an excellent conductor of electricity and heat because its atoms have loosely bound electrons that are free to move. This allows for the easy transfer of heat or electricity throughout the material.
Water is also a good conductor of both heat and electricity. It contains charged particles called ions that can carry electric current. Additionally, water molecules are able to transfer heat through convection.
Copper is widely used in electrical wiring because it is an excellent conductor of electricity. Like silver, its atoms have free electrons that can move easily and transfer electrical energy.
Therefore, rubber is the material that serves as a good insulator, while silver, water, and copper are good conductors of heat and electricity.
Question 29 Report
Which of the following is NOT an example of elementary modern physics?
Answer Details
Classical mechanics is a branch of physics that deals with the motion of macroscopic objects. It is based on the principles of Newton's laws of motion and is not considered to be part of elementary modern physics.
The other three options, quantum mechanics, special relativity, and nuclear physics, are all considered to be part of elementary modern physics because they deal with the behavior of matter and energy at the atomic and subatomic levels.
Question 30 Report
When light of a certain frequency is incident on a metal surface, no photoelectrons are emitted. If the frequency of the light is increased, what happens to the stopping potential?
Answer Details
When light of a certain frequency is incident on a metal surface, no photoelectrons are emitted. This is because the energy of the photons in the light is not enough to overcome the work function of the metal, which is the minimum amount of energy required to remove an electron from the metal surface.
If the frequency of the light is increased, it means that the energy of the photons increases. This increase in energy means that there is now enough energy to overcome the work function of the metal. As a result, photoelectrons are now emitted from the metal surface.
Now, let's consider the stopping potential. The stopping potential is the minimum potential difference that needs to be applied across a pair of electrodes in order to stop the flow of photoelectrons from reaching the other electrode.
When the frequency of the light is increased, the energy of the photons also increases. This means that the photoelectrons have more kinetic energy when they are emitted from the metal surface. As a result, a higher stopping potential is required to stop the more energetic photoelectrons from reaching the other electrode.
Therefore, the stopping potential increases when the frequency of the light is increased.
Question 31 Report
A piano wire 50 cm long has a total mass of 10 g and its stretched with a tension of 800 N. Find the frequency of the wire when it sounds its third overtone note.
Answer Details
T=800N; I=50cm=0.5m,
m=10g=0.01kg
fundamental freq: fo
${}_{}$ =?
fo
${}_{}$ = 121√Tμ
$\frac{1}{21}$
μ =m1
$\frac{}{}$=0.010.5
$\frac{0.01}{0.5}$
⇒ fo
${}_{}$ =12×0.5
$\frac{1}{2\times 0.5}$√8000.02
$\frac{800}{0.02}$
fo
${}_{}$ ⇒√ 40,000
⇒1st overtone = 2fo
${}_{}$ =2×200 = 400Hz
⇒2nd overtone =3fo
${}_{}$ =3×200=600Hz
∴3rd over tone= 4fo
${}_{}$ =4×200=800Hz
Question 32 Report
Find the tension in the two cords shown in the figure above. Neglect the mass of the cords, and assume that the angle is 38° and the mass m is 220 kg
[Take g = 9.8 ms-2]