JAMB UTME - Physics - 2023

A generator manufacturing company accidentally made an AC generator instead of a DC generator. To fix this error,

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An AC generator uses slip rings to transfer the induced current smoothly to the circuit. A DC generator uses split rings to transfer the induced current to the circuit and also convert the induced AC into pulsating DC. So, to convert an AC generator into a DC generator, the slip rings needs to be replaced with split rings.

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.

How much work is done against the gravitational force on a 3.0 kg object when it is carried from the ground floor to the roof of a building, a vertical climb of 240 m?

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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.

A beam of light traveling in water is incident on a glass which is immersed in the water. The incident beam makes an angle of 40o ${\mathrm{<br>}}^{}$ with the normal. Calculate the angle of refraction in the glass.

[Refractive index of water = 1.33, Refractive index of glass = 1.5]

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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 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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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.

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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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**.

An explosion occurs at an altitude of 312 m above the ground. If the air temperature is -10.00°C, how long does it take the sound to reach the ground?

[velocity of sound at 0 deg = 331 ms-1]

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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 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.

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 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.

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.

A missile is launched with a speed of 75 ms-1 at an angle of 22° above the surface of a warship. Find the horizontal range achieved by the missile. Ignore the effects of air resistance.

[Take g = 10 ms-1]

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Which of the following materials is a good insulator?

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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.

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.

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

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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.

The half life of a radioactive material is 12 days. Calculate the decay constant.

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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).

Which of the following liquids has the highest surface tension?

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Surface tension is a property of liquids that arises due to the cohesive forces between the molecules at the surface. It can be thought of as the "skin" or "film" that forms on the surface of a liquid.

Considering the options given:

- Water: Water molecules have strong cohesive forces, allowing them to form hydrogen bonds with each other. As a result, water has relatively high surface tension.

- Mercury: Mercury is a metal with metallic bonding, which is much stronger than the cohesive forces in liquids. As a result, mercury has very high surface tension.

- Oil: Oils typically consist of nonpolar molecules, which have weaker cohesive forces compared to polar molecules like water. Therefore, oil generally has lower surface tension than water.

Based on this information, we can conclude that mercury has the highest surface tension among these liquids.

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.

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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An open-tube mercury manometer is used to measure the pressure in a gas tank. When the atmospheric pressure is 101,325 Pa
, what is the absolute pressure in Pa
 in the tank if the height of the mercury in the open tube is 25 cm higher

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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 terminals of a battery of emf 24.0 V and internal resistance of 1.0 Ω is connected to an external resistor 5.0 Ω. Find the terminal p.d.

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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 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 diagram above illustrates the penetrating power of some types of radiation. X, Y and Z are likely

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The penetrating power of alpha rays, beta rays, and gamma rays varies greatly. Alpha particles can be blocked by a few pieces of paper. Beta particles pass through paper but are stopped by aluminum foil. Gamma rays are the most difficult to stop and require concrete, lead, or other heavy shielding to block them.

Therefore, X = γ-ray; Y = α-particle; Z = β-particle

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.

On a particular hot day, the temperature is 40°C and the partial pressure of water vapor in the air is 38.8 mmHg. What is the relative humidity?

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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.

What is the name of the model of the atom that describes electrons as orbiting the nucleus in specific energy levels?

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The name of the model of the atom that describes electrons as orbiting the nucleus in specific energy levels is the Bohr model.

The Bohr model was proposed by Danish physicist Niels Bohr in 1913. According to this model, electrons revolve around the nucleus in specific energy levels or shells. Each energy level corresponds to a certain amount of energy that an electron possesses. The energy levels are represented by whole numbers, with the closest energy level to the nucleus having the lowest energy and subsequent energy levels having higher energies.

Bohr's model also stated that electrons can only exist in certain fixed orbits around the nucleus. These orbits have a specific distance from the nucleus and are called stationary states. Electrons can move between these energy levels by absorbing or emitting energy in the form of photons.

The Bohr model successfully explained the observed emission and absorption spectra of atoms, as well as the stability of atoms. However, it has limitations in fully describing the behavior of electrons. It does not accurately represent the path or trajectory of electrons and does not account for other quantum effects.

Overall, the Bohr model provides a simplified and understandable framework for visualizing the arrangement of electrons in an atom, with electrons occupying specific energy levels or shells around the nucleus.

Which of the following is NOT an example of elementary modern physics?

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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.

A piano wire 50 cm long has a total mass of 10 g and its stretched with a tension of 800 N. Find the frequency of the wire when it sounds its third overtone note.

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T=800N; I=50cm=0.5m,

m=10g=0.01kg

fundamental freq: fo ${\mathrm{<br>}}_{}$ =?

fo ${\mathrm{<br>}}_{}$ = 121√Tμ $\frac{1}{21}<br>$

μ =m1 $\frac{\mathrm{<br>}}{}$=0.010.5 $\frac{0.01}{0.5}$

⇒ fo ${\mathrm{<br>}}_{}$ =12×0.5 $\frac{1}{2\times 0.5}$√8000.02 $\frac{800}{0.02}$

                  fo ${\mathrm{<br>}}_{}$  ⇒√ 40,000

⇒1st overtone = 2fo ${\mathrm{<br>}}_{}$ =2×200 = 400Hz

⇒2nd overtone =3fo ${\mathrm{<br>}}_{}$ =3×200=600Hz

∴3rd over tone= 4fo ${\mathrm{<br>}}_{}$  =4×200=800Hz

A parallel plate capacitor separated by an air gap is made of 0.8m2 tin plates and 20 mm apart. It is connected to 120 V battery. What is the charge on each plate?

Take εo = 8.85 * 10-12 Fm−1

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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**.

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.

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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.

A man swung an object of mass 2 kg in a circular path with a rope 1.2 m long. If the object was swung at 120 rev/min, find the tension in the rope.

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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.

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.