JAMB UTME - Physics - 2023

In the diagram above, if the south poles of two magnets stroke a steel bar, the polarities at X and Y will respectively be

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The polarities at X and Y would be north and north.

An air bubble of radius 4.5 cm initially at a depth of 12 m below the water surface rises to the surface. If the atmospheric pressure is equal to 10.34 m of water, the radius of the bubble just before it reaches the water surface is

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Which of the following is NOT a limitation of experimental measurements?

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Instrument resolution is not a limitation of experimental measurements. It is the smallest change in a measured quantity that can be detected by an instrument. While instrument resolution limits the accuracy of a measurement, it is not a limitation of experimental measurements itself.

A step-down transformer is used on a 2.2 kV line to deliver 110 V. How many turns are on the primary windings if the secondary has 25 turns?

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To determine the number of turns on the primary winding of a step-down transformer, we need to understand how a transformer works and how the voltage is transformed from the primary to the secondary winding.

A transformer operates on the principle of electromagnetic induction. When an alternating current flows through the primary winding, it creates a changing magnetic field that induces a voltage in the secondary winding.

The voltage ratio between the primary and secondary windings is determined by the ratio of the number of turns in each winding. This means that if we decrease the number of turns in the secondary winding compared to the primary winding, we can reduce the voltage output.

In this case, we are given that the secondary winding has 25 turns and we want to deliver 110 V. The primary winding has a higher voltage, which is 2.2 kV (kilovolts) or 2200 V.

To determine the number of turns on the primary winding, we can set up a simple equation using the voltage ratios:

Primary voltage / Secondary voltage = Primary winding turns / Secondary winding turns

Plugging in the values we have:

2200 V / 110 V = Primary winding turns / 25 turns

Simplifying the equation:

20 = Primary winding turns / 25

To solve for the number of turns on the primary winding, we can cross multiply:

20 x 25 = Primary winding turns

Therefore, the number of turns on the primary winding is 500.

So, the correct answer is 500.

A 35 kΩ is connected in series with a resistance of 40 kΩ. What resistance R must be connected in parallel with the combination so that the equivalent resistance is equal to 25 kΩ?

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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 simple pendulum, has a period of 5.77 seconds. When the pendulum is shortened by 3 m, the period is 4.60 seconds. Calculate the new length of the pendulum

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What is the amount of heat required to raise the temperature of a 0.02 kg of ice cube from −10oC to 10oC ?

[specific latent heat of fusion of ice = 3.34 x 105  Jkg−1, Specific heat capacity of water = 4200 Jkg−1 k−1

Specific heat capacity of ice = 2100 Jkg−1k−1

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A metal sphere is placed on an insulating stand. A negatively charged rod is brought close to it. If the sphere is earthed and the rod is taken away, what will be the charge on the sphere?

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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.

Calculate the absolute pressure at the bottom of a lake at a depth of 32.8 m. Assume the density of the water is 1 x 10-3 kgm-3 and the air above is at a pressure of 101.3 kPa.

[Take g = 9.8 ms-2]

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The electrolyte used in the Nickel-Iron (NiFe) accumulator is

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The electrolyte used in the Nickel-Iron (NiFe) accumulator is **potassium hydroxide solution**.

In a Nickel-Iron accumulator, the electrolyte is the substance that allows the flow of electric current between the electrodes. It is essential for the proper functioning of the accumulator.

Potassium hydroxide solution is the ideal electrolyte for the NiFe accumulator due to its properties. It has good electrical conductivity, which means it allows the movement of ions between the positive and negative electrodes, enabling the flow of electrons and facilitating the charging and discharging process.

In addition to good conductivity, potassium hydroxide solution also has other beneficial properties for the NiFe accumulator. It is stable, ensuring a longer lifespan for the accumulator. It is also less prone to self-discharge, meaning the accumulator can retain its charge for a longer period without significant loss.

Therefore, the electrolyte used in the Nickel-Iron (NiFe) accumulator is potassium hydroxide solution.

Name the type of equilibrium for each position of the ball

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To determine the type of equilibrium for each position of the ball, we need to understand what each type of equilibrium means. 1. **Unstable equilibrium**: This occurs when a small disturbance or change in the system causes the object to move away from its equilibrium position. In other words, the system is "unstable" and will not return to its original position on its own. 2. **Neutral equilibrium**: This occurs when a small disturbance or change in the system does not cause the object to move away from its equilibrium position. The system remains in its new position without any tendency to return to its original position. 3. **Stable equilibrium**: This occurs when a small disturbance or change in the system causes the object to move away from its equilibrium position, but the system has a tendency to return to its original position on its own. Now, let's analyze each position of the ball: A - **Unstable equilibrium**: Suppose the ball is placed at position A. If the ball is slightly disturbed or moved from this position, it will roll away further from its original position and won't come back on its own. Hence, position A is an unstable equilibrium. B - **Stable equilibrium**: Suppose the ball is placed at position B. If the ball is slightly disturbed or moved from this position, it will oscillate back and forth but eventually come back to its original position. This indicates that position B is a stable equilibrium. C - **Neutral equilibrium**: Suppose the ball is placed at position C. If the ball is slightly disturbed or moved from this position, it will stay at the new position without any tendency to return to its original position. This identifies position C as a neutral equilibrium. Based on the explanations above, the correct answer is: A - unstable, B - stable, C - neutral.

A positively charged particle is placed near a negatively charged particle. What is the direction of the electric force between the two particles?

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The correct answer is The electric force is directed from the positive particle to the negative particle.

When a positively charged particle is placed near a negatively charged particle, they exert an attractive force on each other. This force is called the electric force.

According to Coulomb's Law, the electric force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In this case, the positively charged particle has a positive charge and the negatively charged particle has a negative charge. Since opposite charges attract each other, the electric force between them is attractive.

Therefore, the electric force is directed from the positive particle to the negative particle.

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

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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.

From the diagram above, if the potential difference across the resistor, capacitor and inductor are 60V, 120V and 30V respectively, the effective potential difference is

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A travelling wave of amplitude 0.80 m has a frequency of 16 Hz and a wave speed of 20 ms-1

Calculate the wave number of the wave.

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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.

A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Young's modulus for the material of the wire.

[Take g = 10 ms-2]

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The sensitivity of a thermometer is

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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.

The pinhole camera works on

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The pinhole camera works on the principle of the rectilinear propagation of light. This principle states that light travels in straight lines. When light passes through the tiny hole in a pinhole camera, it forms an inverted image on the opposite side of the camera. The size of the image depends on the distance between the object and the pinhole.

Which of the following thermometers measures temperature from the thermal radiation emitted by objects?

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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 near point of a patient's eye is 50.0 cm. What power (in diopters) must a corrective lens have to enable the eye to see clearly an object 25.0 cm away?

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A lorry accelerates uniformly in a straight line with acceleration of 4ms-1 and covers a distance of 250 m in a time interval of 10 s. How far will it travel in the next 10 s?

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Which of the following is an example of a couple?

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A couple is a pair of forces that are equal in magnitude but opposite in direction, and that are applied to a body at different points. The forces of a couple do not produce any translation, but they do produce a rotation.

Rainbow formation is as a result of the combination of which of the following phenomena?
(i) Reflection
(ii) Dispersion
(iii) Total internal reflection
(iv) Refraction

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As light ray enters a drop of water the light is refracted at the surface and at the end of the drop, it is totally internally reflected in which the reflected light returns to the front surface, where it again undergoes refraction as it moves from water to air. The result of this is a dispersed light of colours of different wavelengths.

A charge of 4.6×10−5 $4.6\times {10}^{-}5$C is placed in an electric field of intensity 3.2×104 $3.2\times {10}^4$ Vm−1
. What is the force acting on the electron?

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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**.

Which of the following types of electromagnetic waves is used in night vision goggles?

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Night vision goggles use infrared waves to enable the user to see in the dark.

Infrared waves are a type of electromagnetic radiation that have longer wavelengths than visible light. They fall between the visible and microwave regions on the electromagnetic spectrum. Unlike visible light, which is visible to the human eye, infrared waves cannot be seen without the use of specialized devices such as night vision goggles.

When it is dark, objects do not emit visible light that can be detected by the human eye. However, they do emit heat in the form of infrared radiation. Night vision goggles work by detecting and amplifying this infrared radiation, which is then converted into visible light that can be seen by the user.

The goggles contain an image intensifier tube that is sensitive to infrared radiation. This tube amplifies the incoming infrared light and converts it into an image that can be seen through the goggles. The resulting image appears green because the human eye is more sensitive to green light.

Therefore, to see in the dark, night vision goggles use infrared waves to detect and amplify the infrared radiation emitted by objects. This enables the user to have enhanced vision in low-light conditions or complete darkness.

The pitch of a musical note is determined by the frequency of the sound wave that it produces. If two instruments have the same frequency, which of the following factors will most affect the difference in their pitches?

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The frequency of a sound wave is proportional to the tension of the string. If two instruments have the same frequency, but one has a tighter string, then the instrument with the tighter string will have a higher pitch.

The other factors listed, such as the size of the instrument, the material of the instrument, and the shape of the instrument, will also affect the pitch of the instrument, but they will have a smaller effect than the tension of the string.

The working of the beam balance is based on the principle of

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The working of the beam balance is based on the principle of moments.

Moments, also known as torques, are a measure of the turning effect of a force. In the case of the beam balance, it is the moments that help determine the equilibrium or balance of the system.

The beam balance consists of a beam or lever that is supported at a pivot point called the fulcrum. On either end of the beam, there are pans where the objects to be weighed are placed.

When objects of different weights are placed on the pans, the beam becomes unbalanced. This causes the beam to tilt towards the side with the heavier object. However, in order to achieve equilibrium or balance, the moments on both sides of the beam must be equal.

The moment of a force is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of rotation (the fulcrum) to the line of action of the force.

By adjusting the position of the counterweights or by moving the objects on the pans, the moment on each side of the beam can be balanced, resulting in the beam becoming level or horizontal. This indicates that the weights on both sides are equal.

Therefore, the beam balance operates on the principle of moments, where the balance is achieved by equalizing the moments on both sides of the fulcrum.

Which of the following is a type of incandescent light source?

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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.

Which of the following statements is correct about the angle of dip at various points on Earth?

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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 relative density bottle has a mass of 19 g when empty. When it is completely filled with water, its mass is 66 g. What will be its mass if completely filled with alcohol of relative density 0.8?

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Let mb=mass of empty bottle,

mw ${𝑚}_{𝑤}$=mass of water only and

ma ${𝑚}_{𝑎}$= mass of alcohol only
 

given; mb ${𝑚}_{𝑏}$=19g



mb ${𝑚}_{𝑏}$ + mw ${𝑚}_{𝑤}$ = 66g

mb ${𝑚}_{𝑏}$ + ma ${𝑚}_{𝑎}$ = ?

R.d=0.8

R.d=mass of alcohol

massofalcoholmassofequalvolumeofwater $\frac{𝑚𝑎𝑠𝑠𝑜𝑓𝑎𝑙𝑐𝑜ℎ𝑜𝑙}{𝑚𝑎𝑠𝑠𝑜𝑓𝑒𝑞𝑢𝑎𝑙𝑣𝑜𝑙𝑢𝑚𝑒𝑜𝑓𝑤𝑎𝑡𝑒𝑟}$

mass of equal volume of water = mw ${𝑚}_{𝑤}$=66-19=47g

0.8 = ma47 $\frac{{𝑚}_{𝑎}}{47}$


ma ${𝑚}_{𝑎}$=0.8×47 =37.6g

 mb ${𝑚}_{𝑏}$ + ma ${𝑚}_{𝑎}$ = 19+37.6=56.6g

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

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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 property of wave shown in the diagram above is?

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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.

Three forces with magnitudes 16 N, 12 N and 21 N are shown in the diagram below. Determine the magnitude of their resultant force and angle with the x-axis

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Which of the following is/are not true about the heat capacity of a substance?
(i) It is an intensive property
(ii) Its S.I unit is jK−1
(iii) It is an extensive property
(iv) Its S.I unit is jkg−1

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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.

Which of the following statements regarding the application of electrical conduction via gases is/are correct?
Electrical conduction in gas is applied in:
(i) The identification of gases
(ii) Lighting/fluorescent tubes
(iii) Photocells
(iv) Cathode ray oscilloscope/T.V. tubes

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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

Which process is responsible for production of energy in stars?

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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 number of holes in an intrinsic semiconductor

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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.

How much net work is required to accelerate a 1200 kg car from 10 ms-1 to 15 ms-1

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Which of the following is a type of wave that is both mechanical and longitudinal?

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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.

An object is placed 35 cm away from a convex mirror with a focal length of magnitude 15 cm. What is the location of the image?

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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.