Q. What is the relationship between RMS and average value of an AC waveform? (2023)
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A.
RMS = Average
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B.
RMS = Average × √2
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C.
RMS = Average / √2
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D.
RMS = Average × 2
Solution
For a sinusoidal AC waveform, the RMS value is related to the average value by RMS = Average / √2.
Correct Answer: C — RMS = Average / √2
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Q. What is the relationship between RMS speed and kinetic energy of gas molecules?
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A.
Directly proportional
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B.
Inversely proportional
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C.
No relationship
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D.
Depends on the gas
Solution
The kinetic energy of gas molecules is directly proportional to the square of the RMS speed, as KE = (1/2)mv_rms^2.
Correct Answer: A — Directly proportional
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Q. What is the relationship between RMS speed and molecular weight?
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A.
Directly proportional
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B.
Inversely proportional
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C.
No relation
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D.
Exponential relation
Solution
RMS speed is inversely proportional to the square root of molecular weight.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between shear modulus (G) and Young's modulus (E)?
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A.
G = E / (2(1 + ν))
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B.
G = E * (2(1 + ν))
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C.
G = E / (1 + ν)
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D.
G = E * (1 + ν)
Solution
The relationship is given by G = E / (2(1 + ν)), where ν is Poisson's ratio.
Correct Answer: A — G = E / (2(1 + ν))
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Q. What is the relationship between shear modulus and Young's modulus for isotropic materials?
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A.
G = E/2(1 + ν)
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B.
G = E(1 + ν)/2
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C.
G = E/3
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D.
G = 2E
Solution
The shear modulus (G) is related to Young's modulus (E) and Poisson's ratio (ν) by the formula G = E/2(1 + ν).
Correct Answer: A — G = E/2(1 + ν)
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Q. What is the relationship between shear modulus and Young's modulus?
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A.
They are equal
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B.
Shear modulus is always greater
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C.
Shear modulus is less than Young's modulus
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D.
They are inversely proportional
Solution
Shear modulus is generally less than Young's modulus for most materials.
Correct Answer: C — Shear modulus is less than Young's modulus
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Q. What is the relationship between shear rate and viscosity in a Newtonian fluid?
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A.
Directly proportional
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B.
Inversely proportional
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C.
No relationship
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D.
Exponential relationship
Solution
In a Newtonian fluid, shear stress is directly proportional to shear rate.
Correct Answer: A — Directly proportional
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Q. What is the relationship between shear stress and shear rate in a Newtonian fluid?
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A.
Directly proportional
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B.
Inversely proportional
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C.
Exponential
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D.
No relationship
Solution
In a Newtonian fluid, shear stress is directly proportional to shear rate, which defines its viscosity.
Correct Answer: A — Directly proportional
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Q. What is the relationship between shear stress and shear strain in a material?
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A.
Shear modulus
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B.
Bulk modulus
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C.
Young's modulus
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D.
Poisson's ratio
Solution
The relationship between shear stress and shear strain is defined by the shear modulus.
Correct Answer: A — Shear modulus
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Q. What is the relationship between stress and strain in the elastic limit of a material?
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A.
Directly proportional
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B.
Inversely proportional
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C.
Exponential
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D.
Logarithmic
Solution
Within the elastic limit, stress is directly proportional to strain, as described by Hooke's Law.
Correct Answer: A — Directly proportional
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Q. What is the relationship between stress and strain in the elastic region of a material?
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A.
Stress is directly proportional to strain
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B.
Stress is inversely proportional to strain
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C.
Stress is independent of strain
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D.
Stress is proportional to the square of strain
Solution
In the elastic region, stress is directly proportional to strain, as described by Hooke's Law.
Correct Answer: A — Stress is directly proportional to strain
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Q. What is the relationship between surface tension and temperature for most liquids?
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A.
Directly proportional
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B.
Inversely proportional
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C.
No relationship
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D.
Exponential
Solution
Surface tension is inversely proportional to temperature for most liquids.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between surface tension and the shape of a liquid droplet?
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A.
Droplets are always flat
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B.
Droplets are spherical
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C.
Droplets can be any shape
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D.
Droplets are cubic
Solution
Due to surface tension, liquid droplets tend to minimize their surface area, resulting in a spherical shape.
Correct Answer: B — Droplets are spherical
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Q. What is the relationship between temperature and kinetic energy of gas molecules?
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A.
Directly proportional
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B.
Inversely proportional
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C.
No relationship
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D.
Exponential relationship
Solution
The kinetic energy of gas molecules is directly proportional to the temperature.
Correct Answer: A — Directly proportional
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Q. What is the relationship between temperature and kinetic energy of particles in a substance?
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A.
Directly proportional
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B.
Inversely proportional
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C.
No relationship
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D.
Depends on the substance
Solution
The average kinetic energy of particles in a substance is directly proportional to its temperature.
Correct Answer: A — Directly proportional
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Q. What is the relationship between temperature and kinetic energy of particles?
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A.
Directly proportional
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B.
Inversely proportional
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C.
No relation
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D.
Exponential relation
Solution
The temperature of a substance is directly proportional to the average kinetic energy of its particles.
Correct Answer: A — Directly proportional
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Q. What is the relationship between temperature and the kinetic energy of gas molecules?
-
A.
Directly proportional
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B.
Inversely proportional
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C.
No relationship
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D.
Exponential
Solution
The kinetic energy of gas molecules is directly proportional to the temperature of the gas.
Correct Answer: A — Directly proportional
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Q. What is the relationship between temperature and the rate of a chemical reaction?
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A.
Rate decreases with temperature
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B.
Rate increases with temperature
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C.
Rate is independent of temperature
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D.
Rate is constant at all temperatures
Solution
The rate of a chemical reaction generally increases with an increase in temperature due to higher kinetic energy.
Correct Answer: B — Rate increases with temperature
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Q. What is the relationship between temperature and viscosity for most liquids?
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A.
Viscosity increases with temperature
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B.
Viscosity decreases with temperature
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C.
Viscosity remains constant
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D.
Viscosity fluctuates randomly
Solution
For most liquids, viscosity decreases with an increase in temperature due to increased molecular motion.
Correct Answer: B — Viscosity decreases with temperature
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Q. What is the relationship between temperature and viscosity in liquids?
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A.
Directly proportional
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B.
Inversely proportional
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C.
No relationship
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D.
Exponential
Solution
In general, the viscosity of liquids decreases with an increase in temperature, making them flow more easily.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the amplitude of a damped oscillator and time?
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A.
Exponential decay
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B.
Linear decay
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C.
Quadratic decay
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D.
Constant decay
Solution
The amplitude of a damped oscillator decreases exponentially with time.
Correct Answer: A — Exponential decay
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Q. What is the relationship between the angle of diffraction and the wavelength of light in a single-slit diffraction pattern?
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A.
Directly proportional
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B.
Inversely proportional
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C.
No relationship
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D.
Depends on slit width
Solution
The angle of diffraction is inversely proportional to the wavelength; as the wavelength increases, the angle of diffraction increases.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the angle of incidence and the angle of diffraction in a diffraction grating?
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A.
They are equal
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B.
They are inversely proportional
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C.
They are related by the grating equation
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D.
They are independent
Solution
The angle of incidence and angle of diffraction are related by the grating equation d sin(θ) = mλ.
Correct Answer: C — They are related by the grating equation
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Q. What is the relationship between the angle of incidence and the angle of polarization?
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A.
They are equal
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B.
They are complementary
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C.
They are supplementary
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D.
There is no relationship
Solution
At the angle of polarization, the angle of incidence is equal to the angle of refraction.
Correct Answer: A — They are equal
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Q. What is the relationship between the angle of incidence and the angle of reflection in total internal reflection?
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A.
They are equal
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B.
They are complementary
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C.
They are supplementary
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D.
There is no relationship
Solution
In total internal reflection, the angle of incidence is equal to the angle of reflection.
Correct Answer: A — They are equal
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Q. What is the relationship between the angles of an equilateral triangle? (2023)
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A.
All angles are 60 degrees
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B.
All angles are 90 degrees
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C.
Two angles are equal
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D.
No angles are equal
Solution
In an equilateral triangle, all three angles are equal and measure 60 degrees each.
Correct Answer: A — All angles are 60 degrees
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Q. What is the relationship between the angular velocity (ω) and the linear velocity (v) in circular motion?
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A.
v = ωr
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B.
v = r/ω
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C.
v = ω²r
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D.
v = r²ω
Solution
The relationship is given by v = ωr, where r is the radius of the circular path.
Correct Answer: A — v = ωr
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Q. What is the relationship between the angular velocity and linear velocity of an object moving in a circular path?
-
A.
v = ωr
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B.
v = r/ω
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C.
v = ω/r
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D.
v = ω²r
Solution
Linear velocity (v) is related to angular velocity (ω) by the formula v = ωr.
Correct Answer: A — v = ωr
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Q. What is the relationship between the angular velocity and linear velocity of an object in circular motion?
-
A.
v = ωr
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B.
v = r/ω
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C.
v = ω/r
-
D.
v = ω²r
Solution
Linear velocity (v) is related to angular velocity (ω) by the equation v = ωr.
Correct Answer: A — v = ωr
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Q. What is the relationship between the average kinetic energy of gas molecules and temperature?
-
A.
KE ∝ T
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B.
KE ∝ T^2
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C.
KE ∝ 1/T
-
D.
KE ∝ T^3
Solution
The average kinetic energy of gas molecules is directly proportional to the absolute temperature (KE ∝ T).
Correct Answer: A — KE ∝ T
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