JAMB UTME - Physics - 2024

A mass of gas at 40mmHg is heated from 298k to 348k at constant volume. Cal the pressure exerted by the gas.

Detalles de la respuesta

To determine the new pressure exerted by the gas when it is heated, we'll apply **Gay-Lussac's Law**. This law states that at constant volume, the pressure of a given amount of gas is directly proportional to its absolute temperature. Mathematically, it can be expressed as:

P1/T1 = P2/T2

Where:

• P1 = Initial pressure of the gas (40 mmHg)
• T1 = Initial temperature (298 K)
• P2 = Final pressure of the gas, which we want to find
• T2 = Final temperature (348 K)

By rearranging the formula to solve for the final pressure (P2), we get:

P2 = P1 * (T2/T1)

Now, insert the given values into the equation:

P2 = 40 mmHg * (348 K / 298 K)

Perform the calculations:

P2 = 40 mmHg * (348 / 298)

P2 = 40 mmHg * 1.1678

P2 = 46.71 mmHg

So, the new pressure exerted by the gas when it is heated from 298 K to 348 K at constant volume is 46.71 mmHg.

Detalles de la respuesta

To understand when a vapor is considered saturated, it is crucial to consider the rates of two significant processes: evaporation and condensation. **Evaporation** is the process where liquid molecules escape into the vapor phase, and its rate is denoted as **y**. On the other hand, **condensation** is the process where vapor molecules return to the liquid phase, with its rate denoted as **x**.

A vapor is said to be **saturated** when the rate of evaporation of the liquid is equal to the rate of condensation of the vapor. In simpler terms, the number of molecules leaving the liquid to become vapor is exactly equal to the number of molecules returning from the vapor to the liquid.

In mathematical terms, this condition can be described as **x = y**. Under this condition, the system reaches a dynamic equilibrium, and the vapor pressure of the system is at its maximum for the given temperature. At this point, the vapor cannot accommodate any more molecules, and thus, the vapor is in a saturated state.

The bursting of water pipes during very cold weather, when the water in the pipes form ice could be attributed to 

Detalles de la respuesta

The bursting of water pipes during very cold weather is primarily attributed to the expansion of water on freezing.

Here's why this happens:

1. **Normal water behavior below freezing:** Typically, when most substances freeze, they contract because the molecules get closer together. However, water behaves differently due to its unique molecular structure. As water freezes, it forms a crystalline structure that makes ice less dense than liquid water, causing it to expand.

2. **Effect of expansion:** When water inside a pipe freezes, it expands. This expansion puts tremendous pressure on the pipe walls because the solid ice takes up more space than the liquid water. Most pipes are rigid and do not have enough room to accommodate the expanded volume of ice.

3. **Resulting pressure:** The increased pressure caused by the expanding ice can cause the pipe to crack or burst, especially if there is no other outlet for the water or ice to expand into.

In summary, pipes burst during cold weather primarily due to the expansion of water as it freezes, which creates pressure that the pipe cannot withstand. This phenomenon is due to the unique property of water where it expands upon freezing, unlike most other substances which contract in their solid form.

                               I

6 X  +  6 H2 ${}_2$O      →     C6 ${}_6$H12 ${}_{12}$O6 ${}_6$   +   6O2 ${}_2$ 

 III               chlorophyll      II               IV

Use the diagram above to answer question that follows

The part labelled I is

Detalles de la respuesta

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.

At a pressure of 105 ${}^5$Nm−2 ${}^{-2}$, a gas has a volume of 20m3 ${}^3$. Calculate the volume at 4 x 105 ${}^5$Nm−2 ${}^{-2}$ at constant temperature.

Detalles de la respuesta

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:

• P₁ is the initial pressure: 105 Nm^-2
• V₁ is the initial volume: 20 m³
• P₂ is the final pressure: 4 x 105 Nm^-2
• V₂ is the final volume, which we need to find

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.

If the displacement of a car is proportional to the square of time, then the car is moving with 

Detalles de la respuesta

When we say that the displacement of a car is proportional to the square of time (d ∝ t²), it indicates a relationship between displacement (d) and time (t). This relationship is characteristic of motion where there is constant acceleration. Essentially, it means that the car is not moving at a constant speed (velocity) but is accelerating at a constant rate.

The mathematical representation of this scenario can be expressed using the formula for displacement under uniform acceleration:

d = ut + (1/2)at².

In this equation:

• d = displacement
• u = initial velocity (which could be zero)
• a = acceleration
• t = time

When the displacement is directly proportional to the square of time (d ∝ t²), it implies that the second term of the equation, which contains the (1/2)at² part, dominates the relationship. Thus, the initial velocity (u) is typically zero or negligible, making the entire displacement dependent on how time squared interacts with acceleration.

Therefore, the car is moving with uniform acceleration.

Bifocal lens is used to correct the eye defect of 

Detalles de la respuesta

Bifocal lenses are primarily used to correct the eye defect known as presbyopia. As people age, the lens of the eye naturally loses its flexibility, making it difficult to focus on objects that are close up. This condition is known as presbyopia. A bifocal lens is designed with two different optical powers to accommodate this need. The upper part of the lens is usually crafted for distance vision, while the lower segment is designed for near vision tasks, such as reading.

Astigmatism is a different eye condition caused by irregular curvature of the cornea or lens, resulting in blurred or distorted vision at all distances. This condition is typically corrected with cylindrical lenses rather than bifocals.

Hypermetropia, commonly known as farsightedness, is a condition where distant objects can be seen more clearly than near ones. Simple convex lenses are usually used for this correction.

Myopia, or nearsightedness, is a condition where nearby objects are seen clearly, while distant objects appear blurry. Concave lenses are generally used to correct this condition.

In summary, bifocal lenses are specifically designed to address the challenges of focusing at different distances simultaneously, making them ideal for managing presbyopia.

Which of the following is the best as shaving mirror?

Detalles de la respuesta

When selecting the best type of mirror for shaving, the key consideration is how the mirror reflects light and creates an image. For the purpose of shaving, it is important to have a mirror that magnifies the face and provides a clear view.

The best option for a shaving mirror is a concave mirror. Here is why:

• Magnification: A concave mirror curves inward, similar to the inside of a bowl. When you position your face close to a concave mirror, it produces an enlarged image, making it easier to see details while shaving.
• Focusing Light: Concave mirrors can focus light onto a specific point. This provides a bright and clear image, as the reflected light converges at a point in front of the mirror, enhancing visibility.
• Upright Image: When the object (your face) is placed between the mirror and its focal point, the image remains upright and enlarged. This is perfect for detailed activities like shaving.

Other types of mirrors, like convex and plane mirrors, and parabolic mirrors, do not provide the same level of magnification or focused reflecting properties, making them less suitable for shaving purposes.

The efficiency of a cell with internal resistance of 2Ω $\mathrm{\Omega }$ supply current to a 6Ω $\mathrm{\Omega }$ resistor is 

Detalles de la respuesta

To determine the efficiency of a cell with an internal resistance of 2 Ω while supplying current to a 6 Ω resistor, we can use the concept of power dissipation. Efficiency in this context is the ratio of the power delivered to the external resistor to the total power supplied by the cell. It can be calculated using the formula:

Efficiency (%) = (Power across load resistor / Total power output by cell) × 100

Let's break it down step by step:

• Step 1: Total Resistance - The total resistance in the circuit is the sum of the internal resistance and the resistance of the external resistor:
• Total Resistance (R_total) = Internal Resistance (R_internal) + External Resistance (R_load)
• R_total = 2 Ω + 6 Ω = 8 Ω
• Step 2: Current Calculation - The current flowing through the circuit can be calculated using Ohm's Law, which states V = IR. Assume the electromotive force (EMF) of the cell is E volts:
• Current (I) = E / R_total
• I = E / 8 (Note: We keep E as a variable as it cancels out in the efficiency equation)
• Step 3: Power Delivered to Load - The power delivered to the external resistor can be calculated as:
• Power_load = I² × R_load
• Power_load = (E/8)² × 6
• Step 4: Total Power Supplied by the Cell - The total power supplied by the cell is given by:
• Power_total = EMF × Current = E × (E/8)
• Power_total = E² / 8
• Step 5: Calculate Efficiency: Finally, plug in the power values into the efficiency formula:
• Efficiency (%) = [(E/8)² × 6 / (E² / 8)] × 100
• Simplify to Efficiency (%) = [(6/8)] × 100 = 0.75 × 100 = 75%

The efficiency of the cell when supplying current to a 6 Ω resistor with an internal resistance of 2 Ω is 75%.

When a charged ebonite rod is brought near a charged glass rod, there will be 

Detalles de la respuesta

When a charged ebonite rod is brought near a charged glass rod, there will be attraction. This is because charged objects obey the fundamental principle of electrostatics, which states that opposite charges attract each other while like charges repel each other.

An ebonite rod typically acquires a negative charge when rubbed with fur, as it gains electrons. In contrast, a glass rod usually acquires a positive charge when rubbed with silk, as it loses electrons. Therefore, when these two objects, one negatively charged and the other positively charged, are brought near each other, the opposite charges will attract.

A sonometer's fundamental note is 50Hz, what is the new frequency when the tension is four times the original?

Detalles de la respuesta

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.

Two tuning forks of frequencies 6Hz and 4Hz respectively are sounded together. The beat frequency is 

Detalles de la respuesta

When two sound waves of slightly different frequencies are sounded together, they interfere with each other in such a way that the intensity of the sound alternates between loud and soft. This phenomenon is known as "beats". The number of beats heard per second is called the "beat frequency".

The beat frequency can be calculated by subtracting the frequency of one wave from the frequency of the other. Mathematically, it is represented as:

Beat Frequency (f_beat) = | f₁ - f₂ |

Where:

• f₁ is the frequency of the first tuning fork.
• f₂ is the frequency of the second tuning fork.

In this case:

• f₁ = 6Hz
• f₂ = 4Hz

Using the formula:

f_beat = | 6Hz - 4Hz | = | 2Hz | = 2Hz

Therefore, the beat frequency is 2Hz. This means that you would hear 2 beats per second when the tuning forks of frequencies 6Hz and 4Hz are sounded together.

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?

Detalles de la respuesta

By crossing  Rr  x  rr

We obtain  Rr , rr , rr , Rr

⇒ 50% = 12

The stress experienced by a wire of diameter 

Detalles de la respuesta

Stress is defined as the force applied per unit area. In the context of a wire being loaded by a weight, the weight acts as the force exerted, and the cross-sectional area of the wire is the area over which this force is distributed.

Force (F): This is given by the weight, which is y² N.

Cross-sectional Area (A): For a wire with a diameter, the area can be calculated using the formula for the area of a circle: A = πr², where r is the radius of the wire.

Given the diameter of the wire as yπ meters, the radius (r) is half of the diameter:

r = (yπ)/2

So, the area (A) is:

A = π[(yπ)/2]²

Simplifying the area:

A = π(y²π²/4)
A = y²π³/4

Stress (σ) is given by the formula:

σ = F/A

Substituting the given weight (force) and the calculated area:

σ = (y²) / (y²π³/4)

By simplifying the expression:

σ = (4y²) / (y²π³)

Cancel out y² from numerator and denominator:

σ = 4/π² Nm⁻²

Thus, the correct stress experienced by the wire is 4π Nm⁻², as provided in one of the options. The explanation shows clearly how the force and area are used to derive the stress experienced by the wire.

An effort of 40N is applied on a machine to lift a mass of 60kg. Determine the mechanical advantage of the machine [ g = 10ms2 ${}^2$ ]

Detalles de la respuesta

To determine the Mechanical Advantage (MA) of a machine, we use the formula:

MA = Load / Effort

Here, the Load is the weight of the mass being lifted, and the Effort is the force applied on the machine.

First, we need to calculate the Load. The Load is obtained by multiplying the mass of the object by the acceleration due to gravity (g = 10 m/s²).

So, the Load (weight of the mass) is:

Load = Mass × Gravity = 60 kg × 10 m/s² = 600 N

The Effort given is 40 N.

Now, we can calculate the Mechanical Advantage:

MA = Load / Effort = 600 N / 40 N = 15

Therefore, the Mechanical Advantage of the machine is 15.

A boy standing 408m from a wall blew a trumpet and heard the echo 2.4s later. Calculate the speed of the sound

Detalles de la respuesta

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.

Two capacitors of 0.0003μF and 0.0006μF are connected in series, find their combined capacitance.

Detalles de la respuesta

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.

The energy stored in the above capacitor is 

Detalles de la respuesta

The energy stored in the capacitor = 12 $\frac{1}{2}$q2C $\frac{q^2}{C}$

Where C = 2F, q = 3C

=  12 $\frac{1}{2}$322 $\frac{3^2}{2}$ = 94 $\frac{9}{4}$ = 2.25J

A cell of internal resistance of 2Ω $\mathrm{\Omega }$ supplies current through a resistor, X if the efficiency of the cell is 75%, find the value of X.

Detalles de la respuesta

To solve the problem, let's first understand the concept of efficiency in this context. Efficiency refers to the ratio of the useful power output to the total power output of a system. In simpler terms, it tells us how much of the power provided by the cell is being effectively used by the resistor, X.

Given that the cell has an internal resistance (r) of 2Ω and we need the efficiency to be 75%, we will follow these steps:

• The total resistance in the circuit is the sum of the internal resistance and the resistance of the resistor X, so it is (r + X).
• Efficiency is given by the formula:

Efficiency (%) = (R / (R + r)) * 100

Where:

• R is the resistance of resistor X.
• r is the internal resistance of the cell.

According to the problem, efficiency is 75%, so:

(X / (X + 2)) * 100 = 75

First, let’s eliminate the percentage by dividing both sides by 100:

(X / (X + 2)) = 0.75

Now, let's solve for X:

1. Multiply both sides by (X + 2):

X = 0.75 * (X + 2)



2. Distribute the 0.75:

X = 0.75X + 1.5



3. Subtract 0.75X from both sides:

0.25X = 1.5



4. Finally, divide by 0.25:

X = 1.5 / 0.25



5. Solve for X:

X = 6 Ω

Hence, for the cell to have an efficiency of 75%, the value of the resistor X must be 6Ω.

What is the least possible error encountered when taking measurement with a metre rule?

Detalles de la respuesta

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).

Mouth part adapted for piercing and sucking is found in

Detalles de la respuesta

The mouthpart adapted for piercing and sucking is found in the mosquito. Mosquitoes have a specialized mouth structure called a proboscis. This proboscis is long and slender, allowing mosquitoes to puncture the skin of their hosts and suck blood. The proboscis is a complex structure that contains several needle-like parts that make the piercing and sucking process efficient and effective.

A thick glass tumbler cracks when boiling water is poured into it because

Detalles de la respuesta

When boiling water is poured into a thick glass tumbler, the inner surface of the glass is suddenly exposed to a much higher temperature compared to the outer surface. Glass is a poor conductor of heat, which means it does not transfer heat quickly. As a result, the inside of the tumbler becomes hot and attempts to **expand quickly**, while the outside remains cooler and does not expand at the same rate.

**This uneven expansion** creates tension between the inner and outer layers of the glass. The inner surface tries to expand but is constrained by the cooler, rigid outer surface, which isn't expanding as much or as quickly. This stress and tension can lead to cracking.

Therefore, the correct reason a thick glass tumbler cracks when boiling water is poured into it is because **the inside expands more rapidly than the outside.**

Photometer is used to measure

Detalles de la respuesta

A photometer is an instrument designed to measure the intensity of light. It is used to determine how much light is received over a particular area. Photometers are vital in various fields such as photography, astronomy, and laboratory science for ensuring that light levels are appropriate for specific applications.

The device operates by assessing the brightness or illumination coming from a light source and comparing it with a standard light. The measurement can be displayed in different units such as lumens or lux, depending on the context of the measurement.

While photometers are focused on the intensity of light, they do not measure kinetic energy of liberated electrons, the frequency of light, or the wavelength of light. These quantities are measured using other specialized instruments, such as spectrometers or frequency analyzers.

At absolute zero temperature, the average velocity of the molecules 

Detalles de la respuesta

At absolute zero temperature, which is defined as 0 Kelvin or -273.15 degrees Celsius, the energy of molecular motion ceases. This means that the molecules theoretically have minimal energy, and hence, their motion stops entirely. Therefore, the average velocity of the molecules is zero. In reality, absolute zero is a theoretical limit, and it is practically unreachable, but it serves as a concept to help in understanding the behavior of molecules at extremely low temperatures. Thus, under this theoretical condition, the average motion of molecules would be nonexistent. In summary, the average velocity of the molecules at absolute zero is zero.

In voltage measurement, the potentiometer is preferred to voltmeter because it

Detalles de la respuesta

In voltage measurement, a **potentiometer is preferred to a voltmeter** primarily because it **consumes negligible current**. Let me explain this in simpler terms:

A **voltmeter** is an instrument used to measure the potential difference (voltage) across two points in an electrical circuit. However, when a voltmeter is connected, it draws a small amount of current from the circuit to make the measurement, which can slightly alter the voltage being measured. This is particularly an issue in high-resistance circuits where even a small current draw can significantly affect the measurement.

On the other hand, a **potentiometer** is a device designed to measure voltage by comparing it with a known reference voltage without drawing current from the circuit under test. It comes into balance at a point where no current flows through it, ensuring that the measurement is not influenced by the potentiometer itself. This makes it a non-invasive method of measuring voltage, which is particularly useful for precise measurements in sensitive circuits.

Here’s a brief explanation about why the other options listed are less relevant:

• A **wider range** is not a definitive advantage of potentiometers over voltmeters, as it depends on the settings and design of the specific instrument.
• **Bulkiness** is not a factor that inherently makes a potentiometer preferable; in fact, it can sometimes be a disadvantage due to space constraints.
• **Faster response** is not typically associated with potentiometers compared to voltmeters, as both can be designed to have quick response times depending on the technology used.

Therefore, the key advantage of the potentiometer is its **ability to measure voltage without altering the circuit**, which stems from its negligible current consumption. This **ensures more accurate and reliable measurements** in many applications.

When a bus is accelerating, it must be 

Detalles de la respuesta

When a bus is accelerating, it is primarily changing its velocity. This is because velocity is a vector quantity, which means it includes both the speed and the direction of the object's movement. Acceleration refers to any change in this velocity. Therefore, the bus could be increasing its speed, decreasing its speed (which is also known as deceleration), or changing its direction. All these aspects involve a change in velocity.

Let's break it down further:

Changing its Speed: If the bus is speeding up or slowing down, it results in a change in the magnitude of its velocity, contributing to acceleration.

Changing its Direction: Even if the bus maintains a constant speed, if it changes direction (like taking a turn), its velocity is altered because direction is a part of velocity. This results in acceleration.

Changing its Position: While a change in position happens during acceleration, it is not the defining feature of acceleration. An object can change its position even if it is moving with constant velocity and not accelerating.

So, the key component here for acceleration is the change in velocity, which encompasses changes in speed, direction, or both.

I clear  II sharp  III poor IV dark

Which of the above happens when the hole of a pinhole camera is diminished?

Detalles de la respuesta

A pinhole camera is a simple camera device that uses a tiny hole to project an inverted image of the scene in front of it onto a surface at the back of the camera. When you diminish the hole of a pinhole camera, meaning you make the hole smaller, a few effects occur on the resulting image. Here’s what happens:

• Firstly, when the pinhole is smaller, less light enters the camera. This results in the image becoming darker.
• Additionally, with a smaller hole, the path of light rays becomes narrower which helps to reduce blurring and overlaps from being out of focus. Consequently, the image becomes sharper.

Therefore, reducing the size of the pinhole in a pinhole camera results in the image becoming both darker and sharper.

Answer: II only (The image becomes sharper.)

A blacksmith heated a metal whose cubic expansivity  is 3.9 x 10−6 ${}^{-6}$K−1 ${}^{-1}$. Calculate the area expansivity.

Detalles de la respuesta

To find the area expansivity of a metal when given its cubic expansivity, you should understand the relationship between linear, area, and cubic expansivity.

Cubic expansivity (\( \beta \)) is defined as the fractional change in volume per change in temperature, and is given by the formula:

\[ \Delta V = \beta V \Delta T \]

Area expansivity (\( \alpha_{A} \)) corresponds to the fractional change in area per change in temperature and can be derived from the linear expansivity (\( \alpha \)). The relationship between these expansivities is as follows:

\[ \text{Area Expansivity (\( \alpha_{A} \))} = 2 \times \text{Linear Expansivity (\( \alpha \))} \]

The cubic expansivity (\( \beta \)) is related to the linear expansivity by:

\[ \text{Cubic Expansivity (\( \beta \))} = 3 \times \text{Linear Expansivity (\( \alpha \))} \]

Thus, based on these relationships, we can express the area expansivity in terms of the cubic expansivity:

\(\text{Area Expansivity (\( \alpha_{A} \))} = \frac{2}{3} \times \text{Cubic Expansivity (\( \beta \))}

Given that the cubic expansivity \( \beta \) is \( 3.9 \times 10^{-6} \, \text{K}^{-1} \):

The area expansivity can be calculated as follows:

\[ \text{Area Expansivity (\( \alpha_{A} \))} = \frac{2}{3} \times 3.9 \times 10^{-6} \, \text{K}^{-1} = 2.6 \times 10^{-6} \, \text{K}^{-1} \]

Therefore, the **correct answer** is **2.6 x 10^{-6} K^{-1}**.

Which of the following measuring instruments operates based on the heating effect of electric current?

Detalles de la respuesta

Hot wire ammeters measure current by detecting the heat produced in a wire due to the electric current flowing through it.

The changes of living organisms over generation is referred to as

Detalles de la respuesta

The changes of living organisms over generations are referred to as organic evolution.

Organic evolution, also known as biological evolution, is the process through which species of organisms undergo changes over time due to genetic variations and environmental factors. This leads to the development of new traits and, over long periods, may result in the emergence of new species.

Here's a simple breakdown of the concept:

• **Genetic Variation:** Within a species, individuals have slight genetic differences, primarily due to mutations and the combination of parental genes.
• **Natural Selection:** In any given environment, some traits may offer a survival or reproductive advantage. Organisms with these traits are more likely to pass their genes to the next generation.
• **Adaptation:** Over generations, traits that confer advantages become more common in the population, leading to organisms that are better suited to their environment.
• **Speciation:** With significant changes over long periods, populations may diverge so much that they become new species.

This process is a key concept in biology and is fundamental to understanding the diversity of life on Earth. Organic evolution is distinct from other kinds of evolution mentioned, as it specifically deals with biological organisms.

In electrolysis, when same quantity of electricity is passed through different electrolytes, mass of substances deposited is proportional to 

Detalles de la respuesta

In electrolysis, when the same quantity of electricity is passed through different electrolytes, the mass of substances deposited is proportional to their chemical equivalent. The reason for this lies in Faraday's laws of electrolysis. Faraday's second law states that the amounts of different substances deposited or liberated by the same quantity of electricity are proportional to their chemical equivalents.

Chemical equivalent refers to a measure of a substance's ability to react or be deposited during electrolysis, and it is calculated as the molar mass divided by valency (n). This is why it is sometimes also referred to as equivalent weight.

In essence, for a given charge (equal number of electrons or electricity), a substance with a lower chemical equivalent will deposit more mass because it requires fewer electrons to undergo the chemical change.

In a solar panel, solar beam is concentrated by using 

Detalles de la respuesta

In a solar panel system, the type of mirror used to concentrate solar beams is the Concave Mirror.

Explanation:

A concave mirror is a type of mirror that curves inward, like the inside of a bowl. This shape is very effective at focusing light. When sunlight hits a concave mirror, the mirror's shape causes the light beams to converge, or come together, at a single point known as the focus. This concentrated light can then be used to generate heat or electricity more efficiently.

Why not the others?

A convex mirror curves outward and disperses light beams rather than concentrating them.

A plane mirror has a flat surface and reflects light at the same angle it receives it, meaning it doesn't concentrate the beams.

A triangular mirror is not typically used in solar applications for concentrating light as its shape is not conducive to focusing beams effectively.

Therefore, a concave mirror is best suited for concentrating solar beams in solar panel systems.

An air force jet flying with a speed of 335m/s went past an anti-aircraft gun. How far is the aircraft 5s later when the gun was fired?

Detalles de la respuesta

To solve this problem, we need to determine how far the aircraft travels in the 5 seconds after it passes the anti-aircraft gun. The problem gives us two key pieces of information:

• The speed of the aircraft is 335 m/s.
• The time duration after passing the gun is 5 seconds.

To find the distance traveled, we use the formula for distance:

Distance = Speed × Time

Plugging in the given values:

Distance = 335 m/s × 5 s

Calculating this, we get:

Distance = 1675 meters

This means the aircraft is 1675 meters away from the point where it passed the anti-aircraft gun after 5 seconds.

Under which conditions is work done

Detalles de la respuesta

In physics, the concept of work is defined as the process of energy transfer that occurs when a force makes an object move. The conditions for work to be done are:

• A force must be applied: There must be a force exerted on an object.
• The object must move: The object on which the force is applied must move from its original position.
• The movement must be in the direction of the force: The movement of the object should be in the direction of the applied force.

Now, let's evaluate each scenario:

A man supports a heavy load on his head with hands: In this case, although the man is applying a force upward to support the load, the load does not move in the direction of the force he is exerting (upward). Hence, no work is done.

A woman holds a pot of water: Similar to the first scenario, the woman applies an upward force to hold the pot. However, the pot remains stationary, and there is no movement in the direction of the force. Thus, no work is done.

A boy climbs onto a table: Here, as the boy climbs, he applies a force to move himself upward onto the table. The movement is in the direction of the upward force he is applying. Therefore, work is done.

A man pushes against a stationary petrol tanker: In this scenario, although the man is applying a force to the tanker, it does not move. Because there is no movement in the direction of the force, no work is done.

Two points on a velocity-time graph have coordinates (2s, 5m/s) and (4s, 15m/s). Calculate the mean acceleration

Detalles de la respuesta

The mean acceleration of an object is determined by the change in velocity over the change in time. This is given by the formula:

Mean Acceleration (a) = (Final Velocity - Initial Velocity) / (Final Time - Initial Time)

From the velocity-time graph, we have the following points:

Initial Point: (2s, 5m/s)

Final Point: (4s, 15m/s)

Here, the Initial Velocity is 5m/s, the Final Velocity is 15m/s, the Initial Time is 2s, and the Final Time is 4s.

Plug these values into the formula:

Mean Acceleration (a) = (15m/s - 5m/s) / (4s - 2s)

Simplifying this, we get:

Mean Acceleration (a) = 10m/s / 2s = 5m/s²

The mean acceleration is therefore 5.0 m/s².

A body is pulled on a horizontal surface with a rope inclined at 30º to the vertical. If the effective force pulling the body along the horizontal surface is 15N, calculate the tension on the rope.

Detalles de la respuesta

In this problem, the tension in the rope results in a force that acts to pull the body along the horizontal surface. The rope is inclined at 30º to the vertical, which means it makes an angle of 60º with the horizontal since the total angle between vertical and horizontal is 90º.

To find the tension in the rope, we first understand that the component of the tension force acting along the horizontal surface is given by the formula:

F_horizontal = Tension * cos(θ)

Where:

• F_horizontal is the effective force pulling the body along the horizontal, given as 15N.
• Tension is the total tension in the rope that we need to find.
• θ is the angle of inclination with respect to horizontal = 60º (since the rope is 30º to the vertical, it's 60º to the horizontal).

Given that F_horizontal = 15N, we substitute into the equation:

15N = Tension * cos(60º)

We know that cos(60º) = 0.5, therefore:

15N = Tension * 0.5

To find the Tension, divide both sides of the equation by 0.5:

Tension = 15N / 0.5

Tension = 30N

Therefore, the tension in the rope is 30N.

The gravitational force between two objects  masses 1024 ${}^{24}$kg and 1027 ${}^{27}$kg is 6.67N. Calculate the distance between them [ G = 6.6 x 10−11 ${}^{-11}$Nm2 ${}^2$kg−2 ${}^{-2}$ ]

Detalles de la respuesta

To calculate the distance between two objects based on the gravitational force acting between them, we need to use the formula for gravitational force:

F = (G * m1 * m2) / r²

Where:

• F is the gravitational force between the two masses (6.67 N).
• G is the gravitational constant (6.6 x 10^-11 Nm²/kg²).
• m1 is the first mass (10²⁴ kg).
• m2 is the second mass (10²⁷ kg).
• r is the distance between the centers of the two masses.

We need to compute r by rearranging the formula:

r² = (G * m1 * m2) / F

Therefore, the distance r is:

r = √((G * m1 * m2) / F)

Substitute the given values into the equation:

r = √((6.6 x 10^-11 Nm²/kg² * 10²⁴ kg * 10²⁷ kg) / 6.67 N)

Calculating inside the square root:

G * m1 * m2 = 6.6 x 10^-11 * 10²⁴ * 10²⁷ = 6.6 x 10⁴⁰ Nm²

Then divide by the force:

6.6 x 10⁴⁰ Nm² / 6.67 N = 0.99 x 10⁴⁰ m²

Finally, calculate the square root:

r = √(0.99 x 10⁴⁰)

r ≈ 1.0 x 10²⁰ m

Therefore, the distance between the two objects is approximately 1.0 x 10²⁰ m.

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?

Detalles de la respuesta

For Hare's apparatus

Relative density = hwhl $\frac{h_w}{h_l}$

Given: height of liquid = 0.5cm, height of water = 0.3cm

Relative density = 0.30.5 $\frac{0.3}{0.5}$ = 0.6

The power of a convex lens of focal length 20cm is 

Detalles de la respuesta

The power of a lens is a measure of its ability to converge or diverge light. It is defined as the reciprocal (or inverse) of the focal length of the lens. The formula for calculating the power (P) of a lens in diopters (D) is given by:

P = 1/f

where:

• P is the power of the lens in diopters (D).
• f is the focal length of the lens in meters.

In this case, the focal length given is 20 cm. To apply the formula, we first need to convert this focal length into meters because the diopter is the reciprocal of the focal length in meters:

f = 20 cm = 0.20 m

Now, substitute the focal length in meters into the formula for power:

P = 1 / 0.20

P = 5.00 D

Thus, the power of the convex lens is 5.00 diopters. This indicates that the lens is capable of converging light at a distance of 5.00 meters.

If a body in linear motion changes from point P to Q, the motion is 

Detalles de la respuesta

When a body moves in a straight line from one point, such as point P, to another point, such as point Q, the motion is called Translational Motion. This kind of motion refers to an object moving along a path in which every part of the object takes the same path as a reference point. This means that if you follow any point on the body, it covers the same amount of distance in the same time frame as any other point.

Let's break down the other options:

• Rotational Motion: This occurs when an object spins around an internal axis. For example, the rotation of the Earth on its axis is a rotational motion.


• Simple Harmonic Motion: This is a type of periodic motion where the restoring force is directly proportional to the displacement. An example of this is a pendulum swinging back and forth.


• Circular Motion: This occurs when an object moves along a circular path. For instance, the motion of the planets around the sun is circular motion.

In conclusion, since the body is moving from point P to point Q along a straight line, it exhibits Translational Motion.