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Pergunta 1 Relatório
Name the type of equilibrium for each position of the ball
Detalhes da Resposta
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.
Pergunta 2 Relatório
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 \( \epsilon_o = 8.85 * 10^{-12}\,\mathrm{F\,m^{-1}} \)
Detalhes da Resposta
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**.
Pergunta 3 Relatório
The working of the beam balance is based on the principle of
Detalhes da Resposta
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.
Pergunta 4 Relatório
The number of holes in an intrinsic semiconductor
Detalhes da Resposta
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.
Pergunta 5 Relatório
Light of wavelength 589 nm in vacuum passes through a piece of fused quartz of index of refraction n = 1.458. What is the frequency of the light in fused quartz?
[Speed of light c = 3 *10^8ms-1]
Detalhes da Resposta
Pergunta 6 Relatório
In the diagram above, if the south poles of two magnets stroke a steel bar, the polarities at X and Y will respectively be
Detalhes da Resposta
The polarities at X and Y would be north and north.
Pergunta 7 Relatório
A positively charged particle is placed near a negatively charged particle. What is the direction of the electric force between the two particles?
Detalhes da Resposta
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.
Pergunta 8 Relatório
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.
Detalhes da Resposta
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.
Pergunta 9 Relatório
The pinhole camera works on
Detalhes da Resposta
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.
Pergunta 10 Relatório
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?
Detalhes da Resposta
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.
Pergunta 11 Relatório
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?
Detalhes da Resposta
Let mb=mass of empty bottle,
mw
=mass of water only and
ma
= mass of alcohol only
given; mb
=19g
mb
+ mw
= 66g
mb
+ ma
= ?
R.d=0.8
R.d=mass of alcohol
massofalcoholmassofequalvolumeofwater
mass of equal volume of water = mw
=66-19=47g
0.8 = ma47
ma
=0.8×47 =37.6g
mb
+ ma
= 19+37.6=56.6g
Pergunta 12 Relatório
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?
Detalhes da Resposta
Pergunta 13 Relatório
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
Detalhes da Resposta
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.
Pergunta 14 Relatório
Pergunta 15 Relatório
A generator manufacturing company accidentally made an AC generator instead of a DC generator. To fix this error,
Detalhes da Resposta
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.
Pergunta 16 Relatório
Which of the following materials is a good insulator?
Detalhes da Resposta
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.
Pergunta 17 Relatório
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?
Detalhes da Resposta
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.
Pergunta 18 Relatório
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?
Detalhes da Resposta
For the combination in series;
⇒R1 = 35kΩ + 40kΩ = 75kΩ
R is combined with 75kΩ in parallel to give 25kΩ
= 1Req
= 1R
+ 1R
= 125
= 1R
+ 175
= 125
- 175
+ 1R
= 3−175
= 1R
= 275
= 1R
= 752
= R
; R = 37.5k Ω
Pergunta 19 Relatório
Find the tension in the two cords shown in the figure above. Neglect the mass of the cords, and assume that the angle is 38° and the mass m is 220 kg
[Take g = 9.8 ms-2]
Detalhes da Resposta
W = mg = 220 x 9.8 = 2156 N
⇒Sin 38º = 2156T1
⇒ T1 = 2156Sin38
⇒ T1 = 3502 N
Cos 38º = T2T1
⇒ T2 = 3502 x Cos 38º
⇒ T2 = 2760 N
; T1
= 3502 N, T2
= 2760 N.
Pergunta 20 Relatório
Which of the following types of electromagnetic waves is used in night vision goggles?
Detalhes da Resposta
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.
Pergunta 21 Relatório
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 \(40^\circ\) with the normal. Calculate the angle of refraction in the glass.
[Refractive index of water = 1.33, Refractive index of glass = 1.5]
Pergunta 22 Relatório
Which of the following is NOT a limitation of experimental measurements?
Detalhes da Resposta
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.
Pergunta 23 Relatório
Which of the following statements is correct about the angle of dip at various points on Earth?
Detalhes da Resposta
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.
Pergunta 24 Relatório
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?
Detalhes da Resposta
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.
Pergunta 25 Relatório
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
Pergunta 26 Relatório
A 400 N box is being pushed across a level floor at a constant speed by a force P of 100 N at an angle of 30.0° to the horizontal, as shown in the the diagram below. What is the coefficient of kinetic friction between the box and the floor?
Detalhes da Resposta
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
= μ = 0.19
Pergunta 27 Relatório
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]
Pergunta 28 Relatório
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
Detalhes da Resposta
Pergunta 29 Relatório
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.
Detalhes da Resposta
T=800N; I=50cm=0.5m,
m=10g=0.01kg
fundamental freq: fo
=?
fo
= 121√Tμ
μ =m1
=0.010.5
⇒ fo
=12×0.5
√8000.02
fo
⇒√ 40,000
⇒1st overtone = 2fo
=2×200 = 400Hz
⇒2nd overtone =3fo
=3×200=600Hz
∴3rd over tone= 4fo
=4×200=800Hz
Pergunta 30 Relatório
A travelling wave of amplitude 0.80 m has a frequency of 16 Hz and a wave speed of \(20\ \mathrm{m\,s^{-1}}\).
Calculate the wave number of the wave.
Detalhes da Resposta
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.
Pergunta 31 Relatório
Which of the following is a type of incandescent light source?
Detalhes da Resposta
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.
Pergunta 32 Relatório
Which of the following thermometers measures temperature from the thermal radiation emitted by objects?
Detalhes da Resposta
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.
Pergunta 33 Relatório
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.
Detalhes da Resposta
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.
Pergunta 34 Relatório
An open-tube mercury manometer is used to measure the pressure in a gas tank. When the atmospheric pressure is 101,325 \(P_a\), what is the absolute pressure in \(P_a\) in the tank if the height of the mercury in the open tube is 25 cm higher
Pergunta 35 Relatório
When light of a certain frequency is incident on a metal surface, no photoelectrons are emitted. If the frequency of the light is increased, what happens to the stopping potential?
Detalhes da Resposta
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.
Pergunta 36 Relatório
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
Pergunta 37 Relatório
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]
Pergunta 38 Relatório
The electrolyte used in the Nickel-Iron (NiFe) accumulator is
Detalhes da Resposta
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.
Pergunta 39 Relatório
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?
Detalhes da Resposta
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.
Pergunta 40 Relatório
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
Detalhes da Resposta
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