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Question 1 Report
The gravitational force between two objects is 10N, what is the new value of the force if the distance between them is halved?
Answer Details
The gravitational force between two objects is determined by Newton's Law of Universal Gravitation, which can be expressed by the formula:
F = G * (m1 * m2) / r²
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the centers of the two objects.
In this problem, it is given that the initial gravitational force is 10N. According to the formula, the gravitational force is inversely proportional to the square of the distance between the two objects.
So, if the distance between the objects is halved (i.e., r becomes r/2), then the new gravitational force F' can be calculated based on the relationship:
F' = G * (m1 * m2) / (r/2)² = G * (m1 * m2) / (r²/4) = 4 * (G * m1 * m2 / r²) = 4 * F
Since the initial force F was 10N, the new force F' when the distance is halved is:
F' = 4 * 10 = 40N
Thus, the new value of the gravitational force is 40N.
Question 2 Report
In a Hare's apparatus, the height of water and a liquid X are 0.3m and 0.5m respectively. The relative density of x is?
Answer Details
For Hare's apparatus
Relative density = hwhl
Given: height of liquid = 0.5cm, height of water = 0.3cm
Relative density = 0.30.5 = 0.6
Question 3 Report
In a cross involving a heterozygous red flower plant (Rr) and a white flowered plant (rr). What is the probability that the offspring will be Rr?
Answer Details
By crossing Rr x rr
We obtain Rr , rr , rr , Rr
⇒ 50% = 12
Question 4 Report
The thermometer whose thermometric property is change in volume with temperature is
Answer Details
A thermometer that relies on the **thermometric property** of **change in volume with temperature** is the **Liquid-in-glass thermometer**.
Here is why:
1. **Construction**: A liquid-in-glass thermometer consists of a **glass tube** that encloses a small reservoir filled with a **thermometric liquid**, typically mercury or colored alcohol.
2. **Principle of Operation**: As the **temperature** changes, the **volume of the liquid** inside the tube changes. When the temperature rises, the liquid **expands** and moves up the tube. Conversely, when the temperature decreases, the liquid **contracts** and moves down the tube.
3. **Scale Calibration**: The thermometer has graduations marked along the tube, allowing the user to read the temperature by observing the level of the liquid against these scale markings.
Therefore, the liquid-in-glass thermometer operates on the principle that the **volume of a liquid changes with temperature**, making it the correct answer.
Question 5 Report
A sonometer's fundamental note is 50Hz, what is the new frequency when the tension is four times the original?
Answer Details
To solve this problem, we need to understand the relationship between tension and frequency in a sonometer wire. The frequency of a vibrating string, such as one in a sonometer, is directly proportional to the square root of the tension in the string. Mathematically, this relationship is expressed as:
f ∝ √T
Where f is the frequency and T is the tension. In the given problem, the original frequency is 50 Hz, and the tension is increased to four times its original value. Let's analyze how this change in tension affects the frequency:
- Original tension = T
- New tension = 4T
Substitute the new tension into the formula:
f_new = 50 Hz × √(4T/T)
Simplify the equation:
f_new = 50 Hz × √4
f_new = 50 Hz × 2
f_new = 100 Hz
Thus, when the tension is four times the original tension, the new frequency of the sonometer's fundamental note becomes 100 Hz.
Question 6 Report
Find the amount of current required to deposit 0.02kg of metal in a given electrolysis for 120 seconds. [electro chemical equivalent of the metal = 1.3 x 10−7 kgC−1 ]
Answer Details
To determine the amount of current required, we need to use Faraday's laws of electrolysis. The first law states that the mass of the substance deposited at an electrode is directly proportional to the quantity of electricity (or charge) that passes through the electrolyte.
Here, we have:
According to Faraday's first law of electrolysis, the mass (\( m \)) can be calculated by the formula:
m = z \times I \times t
Where:
Rearranging the formula to solve for current \( I \):
I = \(\frac{m}{z \times t}\)
Substituting the given values into the formula:
I = \(\frac{0.02 \, \text{kg}}{1.3 \times 10^{-7} \, \text{kg/C} \times 120 \, \text{s}}\)
Calculating the denominator:
I = \(\frac{0.02}{1.56 \times 10^{-5}}\)
Solving for \( I \):
I = 1282.05 \, \text{A}
Thus, the appropriate amount of current required to deposit 0.02 kg of metal in 120 seconds is approximately 1.3 x 103 A.
Question 7 Report
At a pressure of 105 Nm−2 , a gas has a volume of 20m3 . Calculate the volume at 4 x 105 Nm−2 at constant temperature.
Answer Details
In order to solve this problem, we can apply **Boyle's Law**, which states that the **pressure** and **volume** of a gas are inversely proportional at a constant temperature. Mathematically, this is expressed as:
P1V1 = P2V2
Where:
Rearranging the formula to solve for V2:
V2 = (P1V1) / P2
Substituting the given values:
V2 = (105 Nm-2 x 20 m3) / (4 x 105 Nm-2)
By calculating:
V2 = (2100 m3) / 4 x 105
V2 = 5 m3
Therefore, at a pressure of 4 x 105 Nm-2, the volume of the gas is 5 m3.
Question 8 Report
If a charge ion goes through a combined electric field E and magnetic field B, the resultant emergent velocity of the ion is
Answer Details
The resultant emergent velocity of a charged ion moving through combined electric and magnetic fields can be derived from the condition where the electric force equals the magnetic force. This gives us the formula for the velocity v:
q E = qvB
v = EB (q will cancel out)
NOTE: When both fields are present, for the ion to move without deflection, the electric force must equal the magnetic force.
Question 9 Report
A solid cube of aluminum is 1.5cm on each edge. The density of aluminum is 2700kgm−1 . Find the mass of the cube.
Answer Details
The mass of an object can be calculated using the formula:
Mass = Density × Volume
In this case, we need to find the mass of a solid cube of aluminum. Given:
First, we need to calculate the volume of the cube. The volume V of a cube with edge length a is given by:
V = a3
Substitute the edge length:
V = (1.5 cm)3 = 1.5 × 1.5 × 1.5 cm3 = 3.375 cm3
Since the density is given in kg/m3, we should convert the volume from cm3 to m3. There are 1,000,000 cm3 in 1 m3, so:
Volume in m3 = 3.375 cm3 × (1 m3/1,000,000 cm3) = 3.375 × 10-6 m3
Now, use the mass formula:
Mass = Density × Volume
Mass = 2700 kg/m3 × 3.375 × 10-6 m3
This equals:
Mass = 9.1125 × 10-3 kg
Convert kg to grams (since 1 kg = 1000 g):
Mass = 9.1125 grams
So, the mass of the cube is approximately 9.1 g. Thus, the correct answer is 9.1 g.
Question 10 Report
Two capacitors of 0.0003μF and 0.0006μF are connected in series, find their combined capacitance.
Answer Details
When capacitors are connected in series, the formula to find their combined capacitance \(C_{\text{total}}\) is given by:
\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \]
where \(C_1\) and \(C_2\) are the capacitances of the individual capacitors. In this case, \(C_1 = 0.0003 \, \mu\text{F}\) and \(C_2 = 0.0006 \, \mu\text{F}\).
First, calculate the reciprocal of each capacitance:
\[ \frac{1}{C_1} = \frac{1}{0.0003} \]
\[ \frac{1}{C_2} = \frac{1}{0.0006} \]
Calculating each value:
\[ \frac{1}{0.0003} = \frac{10^6}{3} \] and \[ \frac{1}{0.0006} = \frac{10^6}{6} \]
Now, add these values together:
\[ \frac{1}{C_{\text{total}}} = \frac{10^6}{3} + \frac{10^6}{6} = \frac{10^6 \times 2}{6} + \frac{10^6 \times 1}{6} = \frac{10^6 \times 3}{6} = \frac{10^6}{2} \]
Finally, take the reciprocal of the resulting value to find \(C_{\text{total}}\):
\[ C_{\text{total}} = \frac{2}{10^6} = 0.0002 \, \mu\text{F} \]
So, the combined capacitance of the two capacitors in series is 0.0002 μF.
Question 11 Report
A light ray passing from air into water at an angle of 30º from the normal in air would
Answer Details
When light passes from one medium to another, such as from air to water, it bends or refracts. This phenomenon is described by Snell's Law, which states: n₁ * sin(θ₁) = n₂ * sin(θ₂), where:
The refractive index of air is approximately 1, and the refractive index of water is approximately 1.33. Given the angle of incidence in air is 30º:
Using Snell's Law:
1 * sin(30º) = 1.33 * sin(θ₂)
You will find:
sin(θ₂) = sin(30º) / 1.33
sin(θ₂) ≈ 0.5 / 1.33
sin(θ₂) ≈ 0.375
Now, solve for θ₂ by taking the inverse sine (arcsin):
θ₂ ≈ arcsin(0.375)
θ₂ ≈ 22.09º
Thus, when a light ray passes from air into water at an angle of 30º from the normal in air, it will make an angle less than 30º from the normal in water, approximately 22.09º. This is because the light ray bends toward the normal as it enters a denser medium (water).
Question 12 Report
A particular household utilizes three electrical appliances for six hours daily if the appliances are rated 80W, 100W, and 120W respectively. Calculate the electrical bills paid monthly if an average month is 31 days. [1kwh = #24.08k]
Answer Details
To calculate the monthly electrical bill, we first need to determine the total energy consumption of the household in kilowatt-hours (kWh). Here are the steps:
1. Calculate the total power consumption of the appliances daily:
2. Convert the daily power consumption from Watts to kilowatts (kW):
3. Calculate the energy used daily in kWh:
4. Calculate the monthly energy consumption:
5. Calculate the cost based on the rate:
Therefore, the monthly electrical bill is approximately ₦1343.66k.
Question 13 Report
What is the least possible error encountered when taking measurement with a metre rule?
Answer Details
A standard meter rule has markings that are usually every millimeter (1 mm). The least count, which is the smallest measurement that can be accurately read, is often 1 mm.
The least possible error is generally considered to be half of the smallest division, so it is ±0.05cm (or ±0.5mm).
Question 14 Report
I
6 X + 6 H2 O → C6 H12 O6 + 6O2
III chlorophyll II IV
Use the diagram above to answer question that follows
The part labelled I is
Answer Details
The part labelled I in the diagram refers to **sunlight**.
Here's a simple explanation:
The given chemical equation is a representation of **photosynthesis**, a process by which green plants, algae, and some bacteria convert light energy, typically from the sun, into chemical energy stored in glucose (C6H12O6) and release oxygen (O2) as a by-product.
In the context of the equation:
- **6CO2 (Carbon Dioxide) + 6H2O (Water) → C6H12O6 (Glucose) + 6O2 (Oxygen)**
The arrow indicates the transformation that occurs during the process. The **chlorophyll** (labelled in the diagram) indicates the presence of chlorophyll pigments in the chloroplasts of plant cells which are essential for **absorbing sunlight**.
Since **sunlight** is the source of energy that powers this transformation, it is the correct component for the part labelled I in the diagram.
Question 15 Report
The tangential force acting on an object that opposes it from sliding freely on the adjacent surface is called
Answer Details
The tangential force acting on an object that opposes it from sliding freely on the adjacent surface is called the friction force.
Let me explain each of the options to clarify why friction force is the correct answer:
In summary, friction force is the force that acts to oppose sliding between surfaces in contact and acts tangentially, making it the correct answer.
Question 16 Report
Use the diagram above to answer the question that follows
The diagram above is
Answer Details
The diagram in the image represents the urinary system, as indicated by the correct answer. The urinary system includes the kidneys, ureters, bladder, and urethra, which are responsible for filtering blood and excreting waste in the form of urine.
Kidneys – Filter waste and excess fluids from the blood to form urine.
Ureters – Tubes that carry urine from the kidneys to the bladder.
Urinary Bladder – Stores urine before it is expelled from the body.
Urethra – A tube that allows urine to exit the body.
This system plays a crucial role in maintaining the body's fluid balance and removing waste products.
Question 17 Report
An accumulator is 90% efficient. If it gives out 2700J of energy while discharging, how much energy does it take in?
Answer Details
In order to find out how much energy the accumulator takes in, given that it is 90% efficient and gives out 2700J of energy, we can use the formula for efficiency:
Efficiency = (Useful Energy Output / Total Energy Input) × 100%
Given:
Efficiency = 90%
Useful Energy Output = 2700J
We need to calculate the Total Energy Input (how much energy the accumulator takes in). Rearranging the formula to solve for Total Energy Input, we get:
Total Energy Input = Useful Energy Output / Efficiency
Substitute the known values:
Total Energy Input = 2700J / 0.9
Calculate the input:
Total Energy Input = 3000J
Therefore, the accumulator takes in 3000J of energy.
Question 18 Report
A body is whirled in a horizontal circle at the rate of 800 revolutions per minute. Determine the angular velocity
Answer Details
To determine the angular velocity of a body whirled in a horizontal circle at a rate of 800 revolutions per minute (rpm), we need to convert this to the standard unit of angular velocity, which is radians per second (rad/s).
Here’s how you can calculate it:
Now let's perform the conversion:
Rounding up the decimal to a consistent significant figure, the angular velocity is approximately 26.7π radians per second.
Question 19 Report
Calculate the power of an object which moves through a distance of 500cm in 1s on a frictionless surface by a horizontal force of 50N
Answer Details
To calculate the power of an object, we need to use the formula for power in terms of work done over time. The formula is:
Power (P) = Work Done (W) / Time (t)
First, let's find the work done on the object. Work done can be calculated using the formula:
Work Done (W) = Force (F) × Distance (d)
Given:
Substituting the values into the formula for work done, we get:
Work Done (W) = 50 N × 5 m = 250 Joules
Next, we consider the time it took for the object to move this distance:
Now, substituting the work done and time into the power formula:
Power (P) = 250 Joules / 1 s = 250 Watts
Thus, the power of the object is 250 Watts.
Question 20 Report
The web-feet of frogs and toads is basically for
Answer Details
The web-feet of frogs and toads is primarily for swimming. These webbed feet act like paddles, allowing the frog or toad to move efficiently through the water. When the animal spreads its toes, the webbing provides a larger surface area, which gives better propulsion in the water. This adaptation is essential, as many species of frogs and toads spend a significant amount of their time in aquatic environments where efficient swimming helps them in searching for food, escaping predators, and traveling from one place to another. In essence, the webbed feet are a vital feature for their aquatic lifestyle.
Question 21 Report
The degree of precision of a vernier caliper is
Answer Details
The degree of precision of a vernier caliper is actually the **smallest value** that the vernier scale can measure, which can be considered as the resolution or least count of the instrument. The degree of precision for most standard vernier calipers is 0.01 cm (or 0.1 mm). This means that the caliper can measure dimensions down to a hundredth of a centimeter.
To understand why this is the case, consider the construction of a vernier caliper:
This alignment allows more precise measurements than the main scale alone. If the vernier scale has 10 divisions which coincide over a length equal to 9 divisions on the main scale, then each division of the vernier scale represents an extra 0.01 cm. Therefore, it allows measuring smaller intervals between the main scale markings very precisely.
Thus, you won't find vernier calipers with a degree of precision of 0.005 cm, 0.1 cm, or 1.0 cm as options in standard practice for precise measurement tools.
Question 22 Report
The quantity of heat required to melt ice of 0.2 kg whose specific latent heat is 3.4 x 105 J/Kg is
Answer Details
To determine the quantity of heat required to melt ice, we use the formula for latent heat:
Q = m × L,
where:
For this problem, we have:
Now, substitute these values into the formula:
Q = 0.2 kg × 3.4 × 105 J/kg
Calculate the product:
Q = 0.68 × 105 J
To express this in standard scientific notation, it can be rewritten as:
Q = 6.8 × 104 J
Thus, the quantity of heat required to melt 0.2 kg of ice is 6.8 × 104 J.
Question 23 Report
Which of the following measuring instruments operates based on the heating effect of electric current?
Answer Details
Hot wire ammeters measure current by detecting the heat produced in a wire due to the electric current flowing through it.
Question 24 Report
The device for measuring the angle of dip is
Answer Details
The device used for measuring the angle of dip is the dip circle.
Let me explain this in simple terms:
The angle of dip, also known as the magnetic inclination, is the angle made by the Earth's magnetic field lines with the horizontal plane. It varies depending on where you are on the Earth's surface. In some places, magnetic field lines are nearly vertical, while in others they are more horizontal.
A dip circle is a specialized scientific instrument used to measure this angle. It usually consists of a magnetic needle that is free to rotate in the vertical plane.
When using a dip circle, you align it so that its plane is parallel to the direction of the Earth's magnetic field. Then, you read the angle at which the magnetic needle stabilizes. This is the angle of dip. The instrument's mechanism allows for accurate measurement of this angle by compensating for any external influences or inclinations.
Question 25 Report
The dimension of power is
Answer Details
The dimension of power in physics is expressed in terms of the base units of mass (M), length (L), and time (T). Power is the rate at which work is done or energy is transferred over time, and it has the unit of watt (W) which is equivalent to one joule per second.
To derive the dimension of power:
1. Work has the dimension of energy, which is force applied over a distance. The dimension of work (or energy) is M L2 T-2 because force has the dimension M L T-2 and distance adds another L.
2. Since power is work done per unit time, you would divide the dimension of work by time (T).
Thus, the dimensional formula for power is:
M L2 T-3
Question 26 Report
The fourth overtone of a closed pipes is 900Hz, its fundamental frequency is
Answer Details
To solve this problem, let's first understand how sound works in a closed pipe. A closed pipe has one end closed and another end open. Sound waves inside such a pipe create standing waves, where nodes (points of no movement) and antinodes (points of maximum movement) are formed.
For a closed pipe, the fundamental frequency (also called the first harmonic) has one node at the closed end and one antinode at the open end. The wavelength is four times the length of the pipe.
The overtone sequence for a closed pipe includes only odd harmonics: 1st (fundamental), 3rd, 5th, 7th, etc. The nth overtone is the 2nth + 1 harmonic. The equation for the frequency of a harmonic in a closed pipe is:
f_n = n * f_1, where f_n is the frequency of the nth harmonic and f_1 is the fundamental frequency
In this case, the fourth overtone corresponds to the 9th harmonic because 2 * 4 + 1 = 9. Therefore, we have:
900 Hz = 9 * f_1
To find the fundamental frequency (f_1), we solve for f_1:
f_1 = 900 Hz / 9
f_1 = 100 Hz
Therefore, the fundamental frequency is 100 Hz.
Question 27 Report
5 X 10−3 kg of liquid at its boiling point is evaporated in 20s by the heat generated by a resistor of 2Ω when a current of 10A is used. The specific latent heat of vaporization of the liquid is
Answer Details
To solve this problem, we need to calculate the specific latent heat of vaporization of the liquid. The specific latent heat of vaporization, denoted as \(L\), is defined as the amount of heat required to convert 1 kilogram of a liquid into a gas at constant temperature and pressure. The formula for specific latent heat of vaporization is given by:
L = \(\frac{Q}{m}\)
Where:
First, we need to calculate the total heat energy \(Q\) generated by the resistor. The heat produced by an electrical resistor can be calculated using the formula:
Q = I^2Rt
Where:
Given:
Substituting these values into the formula for Q:
Q = (10^2) * 2 * 20 = 100 * 2 * 20 = 4000 J
Now that we have the total heat energy supplied, let's calculate the specific latent heat of vaporization:
Given that the mass \(m\) of the liquid evaporated is \(5 \times 10^{-3}\) kg, we can substitute the values into the formula for \(L\):
L = \(\frac{4000}{5 \times 10^{-3}} = \frac{4000}{0.005} = 800,000 J/kg\)
Therefore, the specific latent heat of vaporization of the liquid is 8.0 x 105 J/kg.
Question 28 Report
Which of the following structures enables the exchange of gases in insects?
Answer Details
In insects, the structure responsible for the exchange of gases is the tracheae. Insects have a unique respiratory system where air is taken in through tiny openings called spiracles located on the surface of their body.
The air then travels directly into a network of tubes known as the tracheae. The tracheae branch out extensively throughout the insect's body, allowing oxygen to diffuse directly to the insect's tissues and cells. The carbon dioxide produced in the cells travels back through the tracheae and exits the body through the spiracles.
Other structures like the skin, Malpighian tubules, and flame cells have different functions:
Thus, the correct answer is the tracheae as they specifically enable the exchange of gases in insects.
Question 29 Report
Rainbow is formed when sunlight undergoes
Answer Details
A rainbow is formed through a combination of three processes: reflection, refraction, and dispersion. Let's break down each process to understand how a rainbow forms:
1. Refraction: When sunlight enters a raindrop, it bends or changes direction. This bending of light is known as **refraction**. Different colors of sunlight bend by different amounts because they have different wavelengths.
2. Reflection: Once inside the raindrop, the light gets reflected off the inside surface of the drop. This reflection sends the light back out of the raindrop at different angles.
3. Dispersion: As the light exits the raindrop, it bends again (refraction). Because each color bends by a different amount, the sunlight is spread out into its component colors, creating a spectrum. This spreading into a spectrum is called **dispersion**.
All three processes contribute to the formation of a rainbow. The combination of **refraction, reflection, and dispersion** results in the beautiful arc of colors that we see in the sky.
Question 30 Report
Calculate the magnetic force on an electron in a magnetic field of flux density 10T, with a velocity of 3 x 107 m/s at 60º to the magnetic field (e = 1.6 x 10−19 C)
Answer Details
The magnetic force on an electron in a magnetic field (F) = q v Bsinθ
B = 10T, q = 3 x 107 m/, θ = 60º and q = 1.6 x 10−19 C
F = 1.6 x 10−19 x 3 x 107 x 10 x sin 60º ≊ 4.162 × 10−11 N
Question 31 Report
The moon's acceleration due to gravity is 16 of the earth's value. The weight of a bowling ball on the moon would be
Answer Details
To determine the weight of a bowling ball on the moon, we need to understand the relationship between weight, gravity, and mass.
Weight is the force exerted by gravity on an object. On Earth, this force depends on the object's mass and the acceleration due to gravity, which is approximately 9.8 m/s². Weight can be calculated using the formula:
Weight = Mass x Gravity
On the moon, the acceleration due to gravity is only 1/6 of Earth’s gravity. This means the gravitational pull on the moon is much weaker compared to the Earth. If we take the Earth's gravity to be 9.8 m/s², the moon's gravity would be:
Moon's Gravity = (9.8 m/s²) x (1/6) ≈ 1.63 m/s²
Given that the weight of an object is directly proportional to the gravitational force, the weight of an object on the moon would be substantially less than its weight on Earth. Thus, the weight of the bowling ball on the moon would be:
Weight on Moon = (Mass) x (1.63 m/s²) = 1/6 of its weight on Earth
Therefore, the weight of a bowling ball on the moon is 1/6 of its weight on Earth.
Question 32 Report
The mechanical advantage of the machine shown above
Answer Details
Mechanical advantage of a machine = LOADEFFORT
In this case of a wedge, we can consider the dimensions given:
Load distance (height of the machine): 15 cm
Effort distance (movement of the effort): 0.5 cm
M.A = 150.5 = 30.0
Question 33 Report
Infra-red thermometers work by detecting the
Answer Details
Infra-red thermometers work by detecting the radiation from the body and converting it to temperature. These thermometers are designed to measure the infrared radiation, also known as heat radiation, emitted by objects. All objects with a temperature above absolute zero emit infrared radiation. The thermometer's sensor captures this radiation and converts it into an electrical signal that can be read as a temperature measurement. This method allows for quick, non-contact temperature readings, which is why infrared thermometers are often used in medical settings, industrial applications, and more.
Question 34 Report
A load of 300N is to be lifted by a machine with a velocity ratio of 2 and an efficiency of 60%. What effort will be applied to lift the load?
Answer Details
To determine the effort needed to lift a load using a machine, we first need to understand some key concepts: **Load**, **Effort**, **Velocity Ratio** (VR), and **Efficiency**.
1. **Load** is the force or weight that needs to be lifted by the machine. In this case, the load is 300N.
2. **Velocity Ratio (VR)** is the ratio of the distance moved by the effort to the distance moved by the load. Given here as 2.
3. **Efficiency** of a machine is expressed as a percentage and is the ratio of the useful work output to the input work done by the effort. Here, the efficiency is 60% or 0.60 as a decimal.
The formula to calculate the **Effort** is derived from the relationship between these factors:
\[ \text{Efficiency} = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}} \]
Where:
\[ \text{Mechanical Advantage (MA)} = \frac{\text{Load}}{\text{Effort}} \]
From the above, we have:
\[ \text{MA} = \text{VR} \times \text{Efficiency} \]
Replacing with the given values:
\[ MA = 2 \times 0.60 = 1.2 \]
Now, calculate the **Effort** using the relation:
\[ \text{Effort} = \frac{\text{Load}}{\text{MA}} \]
\[ \text{Effort} = \frac{300N}{1.2} = 250N \]
Therefore, the **Effort** needed to lift the load is 250N.
Question 35 Report
The energy in a moving car is an example of
Answer Details
The energy in a moving car is an example of kinetic energy.
To explain simply, **energy** is the ability to do **work** or cause **change**. There are different forms of energy, and **kinetic energy** is one of them. It is defined as the energy possessed by an object due to its motion.
When a car is moving, it possesses **kinetic energy** because its components are in **motion**. This motion energy allows the car to do tasks, such as transporting people or goods from one place to another. The faster the car moves, the greater its **kinetic energy**, and thus it can make a larger impact or do more work.
In contrast, energy forms like **mechanical energy** is a combination of both kinetic and potential energy; **electrical energy** is associated with electrical charge movement, while **potential energy** is related to the position or condition of an object (like a car parked on a hill). Therefore, the specific type of energy from a moving car is **kinetic energy**.
Question 36 Report
How much joules of heat are given out when a piece of iron, of mass 60g and specific heat capacity 460JKg−1 K−1 , cools from 75ºC to 35ºC
Answer Details
To find out how much heat is given out when the piece of iron cools down, we can use the formula for heat transfer:
Q = mcΔT
Where:
First, let's list the values given and convert the mass from grams to kilograms:
Now, calculate the change in temperature:
ΔT = final temperature - initial temperature = 35ºC - 75ºC = -40ºC
Note: Since we are calculating the heat given out as the iron cools, the temperature change will be negative, which will make Q positive, indicating heat is released.
Substitute these values into the heat transfer formula:
Q = mcΔT = (0.06 kg) x (460 J/Kg·K) x (-40ºC)
Q = 0.06 x 460 x -40
Q = -1104 Joules
Since the question asks for how much heat is given out, we consider the positive value of Q, which is 1104J. Therefore, 1104J of heat is given out when the piece of iron cools from 75ºC to 35ºC.
Question 37 Report
The land and sea breeze is attributed to
Answer Details
The phenomenon of land and sea breeze is primarily attributed to convection.
To understand this, let's first look at what land and sea breezes are:
Land Breeze: At night, the land cools down faster than the sea. The cooler, denser air from the land moves towards the sea, and this is known as a land breeze.
Sea Breeze: During the day, the land heats up more quickly than the sea. The warmer, lighter air over the land rises, and the cooler air from the sea moves in to take its place. This movement of air from the sea to the land is known as a sea breeze.
Both of these processes involve the movement of air due to differences in temperature and density, which is essentially the process of convection.
Convection is the transfer of heat through a fluid (like air or water) and is responsible for moving air masses and creating these breezes. The warm air, being less dense, rises, and the cooler, denser air moves in to replace it.
In contrast, conduction is the transfer of heat through a solid material, and radiation is the transfer of heat in the form of electromagnetic waves, neither of which primarily drive the processes of these breezes, making convection the key player.
Question 38 Report
Which of the following materials has a very large energy gap band?
Answer Details
An insulator is a material that has a very large energy gap between its valence band and conduction band. To understand this, let's first consider the concept of energy bands: In materials, electrons exist in different energy levels. These levels form bands called the valence band and the conduction band. A material is classified based on the size of the energy gap between these bands.
Thus, insulators have a very large energy gap band, making them poor conductors of electricity.
Question 39 Report
A boy standing 408m from a wall blew a trumpet and heard the echo 2.4s later. Calculate the speed of the sound
Answer Details
To calculate the speed of sound, we need to understand that an echo involves a sound wave traveling to a surface and back. In this case, the sound travels from the boy to the wall and then returns.
The total distance that the sound wave travels is twice the distance from the boy to the wall because it goes to the wall and back. Therefore, the total distance is:
Total Distance = 2 x 408m = 816m
The echo was heard 2.4 seconds after the sound was made. The speed of sound can be calculated using the formula:
Speed of Sound = Total Distance / Time
Plugging in the values, we have:
Speed of Sound = 816m / 2.4s
When you perform the division, you find:
Speed of Sound = 340 m/s
Thus, the speed of the sound is 340 m/s, which is the correct answer.
Question 40 Report
The distance between two successive crests of a water wave is 0.25m. If a particle on the surface of the water makes four complete vertical oscillations in one second. Calculate the speed of the wave.
Answer Details
To calculate the speed of the wave, we need to understand some fundamental wave properties: **wavelength**, **frequency**, and **wave speed**.
1. **Wavelength (\( \lambda \))**: The wavelength is the distance between two successive crests of a wave. In this case, the wavelength is given as **0.25 meters**.
2. **Frequency (\( f \))**: Frequency is the number of complete oscillations or cycles that occur per second. It is given that a particle on the surface of the water makes **four complete vertical oscillations in one second**. So, the frequency is **4 Hz (hertz)**.
3. **Wave Speed (\( v \))**: The speed of a wave is calculated using the formula:
\( v = f \times \lambda \)
Where:
\( v \) is the wave speed,
\( f \) is the frequency, and
\( \lambda \) is the wavelength.
Substitute the given values into the formula:
\( v = 4 \text{ Hz} \times 0.25 \text{ m} \)
\( v = 1 \text{ m/s} \)
Therefore, the **speed of the wave** is 1 m/s.
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