JAMB UTME - Physics - 2023

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

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.

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.

To find the tension in the rope, we can first use the formula for centripetal force, which is given by:
F_centripetal = (m * v^2) / r
where: - F_centripetal is the centripetal force - m is the mass of the object - v is the velocity of the object - r is the radius of the circular path
In this case, the mass of the object (m) is given as 2 kg and the radius (r) is given as 1.2 m.
Now, to find the velocity (v), we need to convert the given value of 120 rev/min to m/s.
Here's how we can do that:
1. First, convert the revolutions per minute (rev/min) to revolutions per second (rev/s) by dividing by 60 (since there are 60 seconds in a minute):
120 rev/min = 120/60 rev/s = 2 rev/s
2. Next, we need to convert the revolutions per second to the linear velocity in meters per second (m/s). To do this, we need to find the circumference of the circular path.
The circumference of a circle is given by the formula:
C = 2πr where r is the radius of the circular path.
Substituting the value of the radius (r = 1.2 m) into the formula, we have:
C = 2π * 1.2 = 2.4π Now, to find the linear velocity (v), we can multiply the circumference (C) by the number of revolutions per second (2 rev/s):
v = C * rev/s = 2.4π * 2 = 4.8π m/s
Now that we have the values of m (2 kg) and v (4.8π m/s), we can substitute them into the centripetal force formula to find the tension in the rope:
F_centripetal = (m * v^2) / r = (2 * (4.8π)^2) / 1.2
Simplifying further:
F_centripetal = (2 * 23.04π^2) / 1.2
F_centripetal = 38.4π^2
Finally, to get a numerical value for the tension in the rope, we can approximate the value of π to 3.14 and calculate the centripetal force:
F_centripetal ≈ 38.4 * 3.14^2 ≈ 379 N
Therefore, the tension in the rope is approximately 379 N.
Therefore, the correct answer is 379.

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.

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 $\frac{\mathrm{<br>}}{}$

        = μ = 0.19

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:

1. In the core of a star, high temperatures and pressures cause hydrogen nuclei to collide with enough force to overcome their electric repulsion and merge together.
2. This fusion of hydrogen nuclei results in the formation of helium nuclei.
3. During this fusion process, a very tiny amount of mass is converted into a large amount of energy according to Einstein's famous equation, E=mc². The mass difference is released as energy.
4. This released energy is what provides the heat and light that we observe from the stars.

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.

The Tungsten filament lamp is a type of incandescent light source.

An incandescent light source works by using electricity to heat a filament inside the bulb until it becomes so hot that it emits light. In a tungsten filament lamp, the filament is made of tungsten, which is a metal that has a very high melting point. This allows the filament to get extremely hot without melting.

When an electric current passes through the filament, it heats up and starts to glow, producing visible light. The light emitted by a tungsten filament lamp is actually a result of the high temperature, which causes the atoms in the filament to vibrate and release energy in the form of light.

Incandescent light sources like tungsten filament lamps have been widely used for many years because they produce a warm, yellowish light that is similar to natural sunlight. However, they are not very energy-efficient, as a significant amount of the electrical energy is converted into heat rather than light.

In recent years, there has been a shift towards more energy-efficient alternatives like LED lamps and fluorescent lamps. LED lamps use a different mechanism to produce light, using a semiconductor that emits light when electric current passes through it. Fluorescent lamps use a gas-filled tube that emits ultraviolet light when electric current flows through it, and this ultraviolet light is then converted into visible light by a phosphor coating inside the tube.

So, in summary, the tungsten filament lamp is the type of incandescent light source among the options given. It works by heating a tungsten filament to a very high temperature, causing it to emit light. However, it is less energy-efficient compared to LED and fluorescent lamps.

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.

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).

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.

For the combination in series;

⇒R1 = 35kΩ + 40kΩ = 75kΩ

R is combined with 75kΩ in parallel to give 25kΩ

=  1Req $\frac{\mathrm{<br>}}{}$ = 1R $\frac{\mathrm{<br>}}{}$ + 1R $\frac{\mathrm{<br>}}{}$ 

=   125 $\frac{\mathrm{<br>}}{}$     = 1R $\frac{\mathrm{<br>}}{}$ + 175 $\frac{\mathrm{<br>}}{}$ 

=  125 $\frac{\mathrm{<br>}}{}$     - 175 $\frac{\mathrm{<br>}}{}$ + 1R $\frac{\mathrm{<br>}}{}$ 

=   3−175 $\frac{\mathrm{<br>}}{}$ = 1R $\frac{\mathrm{<br>}}{}$ 

=   275 $\frac{\mathrm{<br>}}{}$   = 1R $\frac{\mathrm{<br>}}{}$ 

=   752 $\frac{\mathrm{<br>}}{}$  = R

;      R = 37.5k Ω

A pyrometer thermometer measures temperature from the thermal radiation emitted by objects.

When objects are heated, they emit thermal radiation, which is a form of electromagnetic radiation. This radiation is primarily in the infrared wavelength range. A pyrometer thermometer is specifically designed to measure the intensity of this thermal radiation and convert it into a temperature reading.

The pyrometer thermometer works based on the principle of measuring the amount of thermal radiation reaching the sensor. This is done using a detector that is sensitive to the infrared wavelength range. The detector absorbs the thermal radiation emitted by the object and generates an electrical signal proportional to the intensity of the radiation.

The electrical signal from the detector is then processed by the thermometer's electronics to calculate and display the corresponding temperature. The calibration of the thermometer ensures accurate temperature readings based on the known relationship between the intensity of thermal radiation and temperature.

Pyrometer thermometers are commonly used in industrial applications where contact-based temperature measurement methods are not feasible or accurate enough. They can measure temperatures of objects from a distance without physically touching them, which makes them suitable for measuring high temperatures, moving objects, or objects in hazardous or inaccessible environments.

Therefore, the pyrometer thermometer is the correct option for measuring temperature from thermal radiation emitted by objects.

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.

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.

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.

The branch of physics that deals with the motion of objects and the forces acting on them is called mechanics.

Mechanics is the foundation of physics that studies how objects move and interact under the influence of forces. It encompasses both the study of the motion of macroscopic objects, such as cars and planets, and the behavior of microscopic particles, such as atoms and molecules.

Mechanics is divided into two main branches:

• Classical mechanics: This branch deals with the motion of objects that are larger than atoms and are not moving near the speed of light. It includes the well-known laws of motion formulated by Sir Isaac Newton, such as Newton's laws of motion, which describe how the velocity and acceleration of an object are related to the forces acting upon it.
• Quantum mechanics: This branch deals with the behavior of particles at the atomic and subatomic levels. It is based on probabilities and wave-particle duality, rather than classical concepts of motion and force. Quantum mechanics is essential for our understanding of the behavior of electrons, photons, and other quantum particles.

Therefore, when referring to the branch of physics that specifically focuses on the motion of objects and the forces acting on them, the correct answer is mechanics.

A wave that is both mechanical and longitudinal is sound waves.

Sound waves are created by the vibration of an object, such as a speaker, which causes the air particles around it to vibrate. These vibrations then travel through the air in the form of a wave.

Sound waves are classified as mechanical waves because they require a medium, such as air, water, or solid objects, to travel through. Without a medium, sound waves cannot propagate.

Furthermore, sound waves are classified as longitudinal waves because the particles in the medium vibrate parallel to the direction of the wave. This means that as the sound wave travels, the particles in the medium move back and forth in the same direction as the wave itself.

In contrast, water waves and seismic waves are mechanical waves, but they are not longitudinal. Water waves are categorized as transverse waves because the particles in the water move up and down at right angles to the direction of the wave. Seismic waves, which include earthquake waves, can be both transverse and longitudinal, but typically the primary seismic waves are classified as transverse waves.

Lastly, light waves are not mechanical waves but rather electromagnetic waves. They do not require a medium to travel through and can propagate in a vacuum, unlike sound waves.

To find the terminal p.d. (potential difference), we need to consider the concept of voltage in a circuit. Voltage is the amount of electrical energy per unit charge provided by a power source, in this case, the battery.

In this problem, we are given:

EMF (electromotive force) of the battery = 24.0 V

Internal resistance of the battery = 1.0 Ω

External resistor = 5.0 Ω

When the battery is connected to the external resistor, a current will flow in the circuit. This current is determined by Ohm's law, which states that the current flowing in a circuit is directly proportional to the voltage applied and inversely proportional to the resistance:

I = V / R

where:

I is the current flowing in the circuit

V is the voltage applied

R is the resistance of the circuit

In this case, the voltage applied is the emf of the battery, and the resistance is the sum of the internal resistance and the external resistor.

We can calculate the current flowing in the circuit:

I = 24.0V / (1.0Ω + 5.0Ω) = 24.0V / 6.0Ω = 4.0A

Now, the terminal p.d. is the voltage drop across the external resistor. We can calculate it using Ohm's law:

V = I * R

Substituting the values:

V = 4.0A * 5.0Ω = 20.0V

Therefore, the terminal p.d. is 20.0V.

The property of the wave shown in the diagram is diffraction.
Diffraction is the bending or spreading out of waves as they encounter an obstacle or pass through an opening. It occurs when waves encounter an obstacle that is comparable in size to their wavelength.
In the diagram, you can see that the wave is encountering an opening or a slit, and as a result, it is spreading out or bending around the edges of the opening. This bending or spreading out is characteristic of diffraction.
Diffraction is an important phenomenon in wave behavior and is observed in various situations, such as when sound waves pass through a doorway or when light waves pass through a narrow slit. It helps us understand how waves interact with obstacles and openings in their path.
In summary, the property of the wave shown in the diagram is diffraction, which is the bending or spreading out of waves as they encounter an obstacle or pass through an opening.

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.

W =  mg  = 220 x 9.8 = 2156 N

⇒Sin 38º = 2156T1 $\frac{\mathrm{<br>}}{}$

⇒ T1 ${\mathrm{<br>}}_{}$ =    2156Sin38

⇒ T1 ${\mathrm{<br>}}_{}$ =     3502 N

 

Cos 38º =  T2T1 $\frac{{\mathrm{<br>}}_{}}{}$

⇒ T2 ${\mathrm{<br>}}_{}$  =   3502 x Cos 38º

⇒ T2 ${\mathrm{<br>}}_{}$ =   2760 N

 

;    T1 ${\mathrm{<br>}}_{}$ =   3502 N,  T2
 = 2760 N.

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**.

Let's understand how a convex mirror forms images. In a convex mirror, the center of curvature and the focal point lie behind the mirror. Convex mirrors always produce virtual, upright, and diminished images.
Here, we are given that the object is placed 35 cm away from the convex mirror and the mirror has a focal length of 15 cm.
To find the location of the image, we can use the mirror formula, which states:
1/f = 1/v - 1/u
Where: - f is the focal length of the mirror, - v is the distance of the image from the mirror (negative for virtual image), - u is the distance of the object from the mirror (negative for real object in front of the mirror).
In this case, f = 15 cm and u = -35 cm (negative because the object is in front of the mirror).
Substituting these values into the formula, we get:
1/15 = 1/v - 1/-35
Simplifying the equation, we get:
1/v = 1/15 + 1/35
To add the fractions, we find the common denominator, which is 105. Then, we have:
1/v = (7 + 3)/105
1/v = 10/105
Simplifying further, we get:
1/v = 2/21
To solve for v, we take the reciprocal on both sides of the equation:
v = 21/2
Therefore, the location of the image is 10.5 cm behind the mirror.

In an AC circuit, resonance occurs when the impedance of the circuit is minimum.

Impedance is the total opposition to the flow of alternating current in a circuit, and it consists of two components: resistance (R) and reactance (X).

Reactance can be further divided into two types: inductive reactance (XL) and capacitive reactance (XC).

At resonance, the inductive reactance and the capacitive reactance are equal in magnitude and opposite in sign. This means that their effects cancel each other out, resulting in a minimum total reactance.

Since impedance is the combination of resistance and reactance, when the reactance is at its minimum, the impedance of the circuit is also at its minimum.

So, in summary, resonance occurs in an AC circuit when the impedance is minimum. At resonance, the inductive reactance and the capacitive reactance cancel each other out, resulting in a minimum total reactance and minimum impedance.

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.

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**.

When a water droplet is placed on a freshly cut piece of wood, it spreads out to form a thin layer because the wood is adhesive to water.

Adhesion is the attraction between different substances, in this case, water and wood. Wood is a porous material, meaning it has tiny holes or gaps in its surface. These tiny holes create a large surface area for the water droplet to interact with.

When the water droplet comes into contact with the wood, the adhesive forces between the water molecules and the wood molecules are stronger than the cohesive forces between the water molecules. This causes the water droplet to spread out, trying to maximize its contact with the wood surface.

The spreading out of the water droplet forms a thin layer because the wood surface is not completely smooth. Instead, it has irregularities and imperfections, which allow the water to seep into those gaps and spread out further.

Therefore, when a water droplet is placed on a freshly cut piece of wood, it spreads out to form a thin layer due to the adhesive forces between the water and the wood surface.

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:

- Soapy water: Soapy water contains soap molecules that can disrupt the cohesive forces between water molecules, reducing the surface tension. Therefore, soapy water is likely to have a lower surface tension compared to other liquids.

- 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.

When a negatively charged rod is brought close to a metal sphere, the free electrons in the sphere are repelled from the rod and move to the other end of the sphere. This creates a region of positive charge on the side of the sphere closest to the rod, and a region of negative charge on the opposite side. The process of charge distribution stops when the net force on the free electrons inside the metal is equal to zero.

If the sphere is then earthed, the free electrons will flow from the sphere to the ground, leaving the sphere with a net positive charge.