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Past Questions
What type of vibrations are produced in a sitar wire?
A)
Progressive transverse
B)
Progressive longitudinal
C)
Stationary transverse
D)
Stationary longitudinal
To determine the type of vibrations in a sitar wire, we analyze two characteristics: the direction of vibration and the nature of the wave propagation.
1. **Transverse vs. Longitudinal**: In a string instrument like a sitar, the wire is plucked. The particles of the string move perpendicular (at right angles) to the direction of the wave propagation along the length of the string. This is the definition of a transverse wave. Longitudinal waves (like sound waves in air) involve particles moving parallel to the direction of propagation, which does not happen in a stretched string.
2. **Stationary (Standing) vs. Progressive**: A sitar wire is fixed at both ends. When plucked, waves travel to the ends and reflect back. The superposition of the incident wave and the reflected wave of the same frequency and amplitude creates a 'standing wave' or 'stationary wave'. In a stationary wave, certain points (nodes) remain motionless while others (antinodes) vibrate with maximum amplitude, and the wave does not transport energy forward along the string.
Therefore, the vibrations in a sitar wire are stationary transverse waves.
Which of the following produces a plane wave front?
A)
Point source
B)
Line source
C)
Extended source
D)
None of the above
A wavefront is a surface over which the phase of the wave is constant. Different types of sources produce different types of wavefronts:
1. **Point Source**: A point source emits waves equally in all directions. The resulting wavefronts are concentric spheres, known as **Spherical Wavefronts**. (Option a is incorrect).
2. **Line Source**: A linear source (like a long thin glowing wire) produces wavefronts that are concentric cylinders, known as **Cylindrical Wavefronts**. (Option b is incorrect).
3. **Extended Source**: An extended source is essentially a collection of many point sources. The resulting wavefront is a superposition of many spherical wavefronts, which generally does not result in a plane wavefront unless specific conditions (like distance) are met. (Option c is incorrect).
**What produces a Plane Wavefront?**
A plane wavefront is produced when a spherical wavefront from a distant source (at infinity) reaches a point. As the radius of the sphere becomes infinitely large, the curvature becomes negligible, and the wavefront appears as a plane. Therefore, none of the sources listed (point, line, or extended) inherently produce a plane wavefront at their origin; a plane wavefront is an approximation of a spherical wavefront from a source at an infinite distance.
LASER is a device for
A)
producing a beam of white light
B)
producing a beam of monochromatic and coherent light
C)
producing a beam of high intensity incoherent light
D)
producing a beam of highly penetrating X-rays
LASER stands for 'Light Amplification by Stimulated Emission of Radiation'. It is characterized by three primary properties:
1. Monochromaticity: The light consists of a single wavelength (one color), unlike white light which is a mixture of many wavelengths.
2. Coherence: The light waves are in phase both spatially and temporally, meaning the peaks and troughs of the waves align perfectly.
3. Directionality/Collimation: The beam spreads very little over long distances.
Evaluating the options:
- Option (a) is incorrect because white light is polychromatic (contains many colors), whereas lasers are monochromatic.
- Option (b) is correct as it accurately describes the fundamental properties of laser light.
- Option (c) is incorrect because lasers produce coherent light, not incoherent light.
- Option (d) is incorrect because lasers typically produce visible, infrared, or ultraviolet light; X-rays are produced by different mechanisms (like X-ray tubes or synchrotrons), although 'X-ray lasers' exist as specialized research tools, the general definition of a LASER device refers to the properties of coherence and monochromaticity.
In case of linearly polarized light, the magnitude of the electric field vector
A)
is parallel to the direction of propagation
B)
does not change with time
C)
increases and decreases linearly with time
D)
varies periodically with time
Linearly polarized light is an electromagnetic wave where the electric field vector (E) oscillates in a single fixed plane perpendicular to the direction of propagation. The mathematical expression for the electric field of a linearly polarized wave is E = E₀ sin(kz - ωt), where E₀ is the amplitude, k is the wave number, and ω is the angular frequency.
1. Analysis of Option (a): The electric field vector is always perpendicular (transverse) to the direction of propagation in electromagnetic waves, not parallel. Thus, (a) is incorrect.
2. Analysis of Option (b): The electric field is an oscillating wave; its magnitude changes constantly as the wave passes a point. It is not constant. Thus, (b) is incorrect.
3. Analysis of Option (c): The magnitude varies sinusoidally (following a sine or cosine function), not linearly. A linear change would imply a triangle wave, which is not the nature of light waves. Thus, (c) is incorrect.
4. Analysis of Option (d): Because the electric field follows a sinusoidal function (sin(ωt)), it repeats its value at regular intervals of time (T = 2π/ω). This is the definition of periodic variation. Therefore, (d) is correct.
The temperature of the sun (5000ºC) is measured with
A)
Platinum resistance thermometer
B)
Gas thermometer
C)
Pyrometer
D)
Vapour pressure thermometer
The measurement of temperature depends on the range of the temperature being measured.
1. **Pyrometer (Correct):** A pyrometer is a non-contact temperature sensor that measures the thermal radiation emitted by an object. It is specifically designed for very high temperatures (typically above 1000°C) where physical contact with the object would destroy the sensor or is physically impossible (such as measuring the temperature of the sun or a blast furnace). Since the sun's temperature is approximately 5000°C, a pyrometer is the only viable instrument among the choices.
2. **Platinum Resistance Thermometer (Incorrect):** These operate on the principle that the electrical resistance of platinum increases with temperature. They are highly accurate but are limited to a range of approximately -200°C to 850°C.
3. **Gas Thermometer (Incorrect):** These use the pressure or volume of a gas as the thermometric property. While they are used as primary standards for calibrating other thermometers, they cannot be used to measure the temperature of the sun due to the requirement of a contained gas volume in contact with the heat source.
4. **Vapour Pressure Thermometer (Incorrect):** These measure temperature based on the pressure of a saturated vapor. They are typically used for lower temperature ranges and cannot withstand or measure the extreme temperatures of stars.
In which process, the PV-diagram is a straight line parallel to volume axis?
A)
Isothermal
B)
Isobaric
C)
Irreversible
D)
Adiabatic
In a PV-diagram, the vertical axis (y-axis) represents Pressure (P) and the horizontal axis (x-axis) represents Volume (V). A straight line parallel to the volume axis implies that as the volume changes, the pressure remains constant. A process occurring at constant pressure is defined as an 'Isobaric' process.
Analysis of other options:
- Isothermal: For an ideal gas, PV = constant. The PV-diagram is a hyperbola, not a straight line.
- Adiabatic: For an adiabatic process, PV^γ = constant. This is also a curve (steeper than an isothermal curve), not a straight line parallel to an axis.
- Irreversible: This describes the nature of the process (non-equilibrium) rather than a specific path on a PV-diagram; it is often represented as a dashed line or a sudden jump, but it is not defined by being parallel to the volume axis.
A rocket is fired from the earth to the moon. The distance between the earth and the moon is r and the mass of the earth is 81 times the mass of the moon. The gravitational force on the rocket will be zero, when its distance from the moon is
A)
r/20
B)
r/15
C)
r/10
D)
r/5
To find the point where the gravitational force on the rocket is zero, the gravitational pull from the Earth must be equal and opposite to the gravitational pull from the Moon.
1. Let $M_e$ be the mass of the Earth and $M_m$ be the mass of the Moon.
2. Given: $M_e = 81 M_m$.
3. Let $r$ be the total distance between the Earth and the Moon.
4. Let $x$ be the distance of the rocket from the Moon. Therefore, the distance of the rocket from the Earth is $(r - x)$.
5. At the point where the net force is zero:
$F_{earth} = F_{moon}$
$rac{G M_e m}{(r - x)^2} = rac{G M_m m}{x^2}$
6. Simplifying the equation by canceling $G$ and $m$ (mass of the rocket):
$rac{M_e}{(r - x)^2} = rac{M_m}{x^2}$
7. Substitute $M_e = 81 M_m$:
$rac{81 M_m}{(r - x)^2} = rac{M_m}{x^2}$
$rac{81}{(r - x)^2} = rac{1}{x^2}$
8. Taking the square root of both sides:
$rac{9}{r - x} = rac{1}{x}$
9. Solving for $x$:
$9x = r - x$
$10x = r$
$x = r/10$
Thus, the gravitational force on the rocket will be zero when its distance from the moon is $r/10$.
Ultrasonic waves are used for stirring liquid solutions, because
A)
they do not produce noise during the operation
B)
they are easy to produce
C)
they can produce perfectly homogeneous solutions
D)
they do not produce chemical reaction in the solution
Ultrasonic waves (sound waves with frequencies higher than the upper audible limit of human hearing, typically > 20 kHz) are used for stirring and mixing liquids through a process called 'Ultrasonic Homogenization' or 'Sonication'.
1. **Mechanism (Acoustic Cavitation):** When ultrasonic waves pass through a liquid, they create alternating regions of high pressure (compression) and low pressure (rarefaction). During the low-pressure cycle, tiny vacuum bubbles or cavities are formed. When these bubbles collapse violently during the high-pressure cycle, they release intense local energy and create powerful micro-jets and shock waves.
2. **Effect on Solutions:** This process breaks down particles, droplets, and aggregates into extremely small sizes (nanoscale) and distributes them uniformly throughout the liquid. This results in a perfectly homogeneous solution or emulsion that is far more stable and uniform than what can be achieved with mechanical stirring.
**Analysis of other options:**
- **Option a:** While they are inaudible to humans, the process of cavitation can produce audible noise (sub-harmonics) and the lack of noise is not the primary scientific reason for their use in stirring.
- **Option b:** Producing high-frequency ultrasonic waves requires specialized piezoelectric transducers; they are not necessarily 'easier' to produce than standard mechanical stirring.
- **Option d:** In some cases, sonication can actually trigger chemical reactions (sonochemistry) due to the extreme local temperatures and pressures created during cavitation, so this statement is not universally true nor the reason for their use in stirring.
The equation of state for n moles of an ideal gas is PV=nRT, where R is a constant. The S.I. unit for R is
A)
J K-1 per molecules
B)
J Kg-1K-1
C)
J K-1 mol-1
D)
J K-1g-1
To find the S.I. unit of the universal gas constant R, we rearrange the ideal gas equation PV = nRT to solve for R: R = PV / (nT). Now, we substitute the S.I. units for each variable:
1. P (Pressure) is measured in Pascals (Pa), where 1 Pa = 1 N/m².
2. V (Volume) is measured in cubic meters (m³).
3. n (Amount of substance) is measured in moles (mol).
4. T (Temperature) is measured in Kelvin (K).
Substituting these into the formula:
Unit of R = (Pa * m³) / (mol * K)
Since Pa = N/m², the unit becomes:
Unit of R = ((N/m²) * m³) / (mol * K) = (N * m) / (mol * K).
Since 1 Newton-meter (N*m) is equal to 1 Joule (J), the unit simplifies to:
Unit of R = J / (mol * K) or J mol⁻¹ K⁻¹ (which is equivalent to J K⁻¹ mol⁻¹).
Comparing this to the options:
- Option (a) refers to the Boltzmann constant (k), not the universal gas constant R.
- Option (b) and (d) use mass (Kg or g) instead of moles, which would be the unit for the specific gas constant (R_specific = R/M), not the universal gas constant R.
Avogadro number is the number of molecules in
A)
one litre of gas at N.T.P
B)
one mole of a gas
C)
one gram of a gas
D)
one kilogram of a gas
Avogadro's number (denoted as Nₐ) is a fundamental constant in chemistry and physics. It is defined as the number of constituent particles (usually atoms or molecules) contained in one mole of a substance. The value is approximately 6.022 × 10²³ particles per mole.
Analysis of options:
- Option (a): One litre of gas at N.T.P. does not contain Avogadro's number of molecules. According to the molar volume of an ideal gas, one mole of gas at N.T.P. occupies approximately 22.4 litres. Therefore, one litre contains only 1/22.4 of Avogadro's number.
- Option (b): This is the correct definition. One mole of any substance contains exactly Avogadro's number of particles.
- Option (c) and (d): The number of molecules in one gram or one kilogram depends on the molar mass of the specific gas. For example, one gram of Hydrogen (H₂) contains far more molecules than one gram of Oxygen (O₂). Only the 'mole' provides a constant number of particles regardless of the substance's mass.
Theory of relativity shows that Newtonian mechanics is true
A)
approximately for all velocities
B)
approximately for low velocities
C)
approximately for high velocities
D)
wholly
The Special Theory of Relativity, proposed by Albert Einstein, generalizes the laws of physics to include objects moving at speeds close to the speed of light (c). According to relativity, the Lorentz factor γ = 1 / sqrt(1 - v²/c²) determines the magnitude of relativistic effects such as time dilation and length contraction. When the velocity (v) is very small compared to the speed of light (v << c), the term v²/c² becomes negligible (approximately 0), and γ becomes approximately 1. In this limit, the relativistic equations reduce exactly to the classical equations of Newtonian mechanics. Therefore, Newtonian mechanics is not 'wholly' true (as it fails at high speeds) nor is it true for high velocities; it serves as a highly accurate approximation for the 'low velocity' regime encountered in everyday human experience.
The solar constant of a planet is S. The surface temperature of the sun is T K. The sun subtends as angle q at the planet. Then
A)
S ∝ T^4
B)
S ∝ T^2
C)
S ∝ q^3
D)
S ∝ q
1. The solar constant (S) is defined as the amount of solar energy per unit time received per unit area at the average distance of the planet from the sun.
2. According to the Stefan-Boltzmann Law, the total power radiated per unit area (emissive power) of a blackbody (the sun) is given by E = σT⁴, where σ is the Stefan-Boltzmann constant and T is the absolute temperature of the surface.
3. The total luminosity (L) of the sun is the product of its surface area (4πR² where R is the radius of the sun) and its emissive power: L = (4πR²) * (σT⁴).
4. The solar constant (S) is the luminosity spread over the surface area of a sphere with a radius equal to the distance (d) between the sun and the planet: S = L / (4πd²).
5. Substituting the expression for L: S = (4πR²σT⁴) / (4πd²) = (R²/d²)σT⁴.
6. Since R, d, and σ are constants for a specific planet-sun system, the relationship simplifies to S ∝ T⁴.
7. Regarding the angle θ (the angular diameter of the sun as seen from the planet), θ ≈ 2R/d. While S is proportional to θ²T⁴, the options provided ask for the relationship between S and T or S and θ. The most fundamental thermodynamic relationship given is S ∝ T⁴.
Michelson Morley experiment proved that
A)
earth is an inertial
B)
a non-inertial frame
C)
there is no preferred frame like other
D)
speed of light is same in all inertial frames
The Michelson-Morley experiment (1887) was designed to detect the 'luminiferous ether,' a hypothetical medium through which light waves were thought to propagate. If the ether existed, the speed of light would vary depending on the Earth's motion relative to the ether (creating an 'ether wind'). The experiment yielded a 'null result,' meaning no such difference in speed was detected regardless of the direction of the apparatus or the Earth's orbital motion. This result fundamentally proved that the speed of light is constant (invariant) in all inertial frames of reference, regardless of the motion of the source or the observer. This discovery served as one of the primary empirical foundations for Albert Einstein's Special Theory of Relativity. Option (a) and (b) refer to the nature of the frame, which was not the primary proof of the experiment. Option (c) is a consequence of the result, but the direct physical proof was the constancy of the speed of light.
Which of the following phenomena is responsible for the production of shadow?
A)
Interference of light
B)
Diffraction of light
C)
Polarization of light
D)
Rectilinear propagation of light
Step-by-step reasoning: 1. A shadow is formed when an opaque object is placed in the path of light rays, blocking them from reaching a surface. 2. This occurs because light travels in straight lines in a homogeneous medium, a property known as 'Rectilinear Propagation of Light'. 3. Because light cannot 'bend' around the object to fill the space behind it, a dark region (the shadow) is created.
Why other options are incorrect:
- Interference (a) is the superposition of two or more coherent light waves resulting in a new wave pattern.
- Diffraction (b) is actually the bending of light around corners or through slits; if diffraction were the dominant effect, shadows would be blurred or non-existent because light would bend into the shadowed region.
- Polarization (c) refers to the orientation of the oscillations of light waves and does not cause the blocking of light required to form a shadow.
Wien’s displacement law fails at
A)
low temperature
B)
high temperature
C)
short wavelength
D)
long wavelength
Wien law approximates Planck at short λ, fails at long wavelengths where Rayleigh-Jeans dominates.
The Clausius–Clapeyron equation indicates that an increase in pressure increases the melting point, in case of
A)
all substances
B)
substances which expand on solidification
C)
substances which contract on solidification
D)
substances which neither expand nor contract on solidification
The Clausius-Clapeyron equation describes the slope of the phase boundary between two phases of a substance. For the solid-liquid transition (melting), the equation is given by: dT/dP = T(V_liquid - V_solid) / L, where T is the temperature, P is the pressure, V_liquid is the molar volume of the liquid, V_solid is the molar volume of the solid, and L is the latent heat of fusion (which is always positive).
1. If a substance contracts on solidification, it means the solid is denser than the liquid (V_solid < V_liquid). In this case, (V_liquid - V_solid) is positive. Therefore, dT/dP > 0, meaning an increase in pressure (dP > 0) leads to an increase in the melting point (dT > 0).
2. If a substance expands on solidification (like ice/water), V_solid > V_liquid. In this case, (V_liquid - V_solid) is negative, and dT/dP < 0, meaning an increase in pressure decreases the melting point.
3. Since the question asks for the condition where an increase in pressure increases the melting point, the substance must contract upon solidification (or conversely, expand upon melting).
In Galilean transformations, time interval is
A)
different for different frames
B)
vectors
C)
relative
D)
same for all frames
Galilean transformations are based on the principles of classical (Newtonian) mechanics. One of the fundamental postulates of these transformations is the concept of 'Absolute Time'. In this framework, time is assumed to flow uniformly and identically for all observers, regardless of their state of motion or their frame of reference. Mathematically, if we have two inertial frames S and S' where S' is moving with a constant velocity v relative to S, the transformation for time is expressed as t' = t. This implies that the time interval Δt = t2 - t1 is equal to the time interval Δt' = t'2 - t'1 in all inertial frames.
Analysis of other options:
- Option (a) and (c): These describe 'Relative Time' or 'Time Dilation', which are concepts introduced by Albert Einstein's Special Theory of Relativity (Lorentz Transformations), not Galilean transformations.
- Option (b): Time is a scalar quantity, not a vector, as it has magnitude but no spatial direction.
For observing a cricket match, binocular is preferred to terrestrial telescope for the reason that
A)
the binocular is very easy to handle
B)
the binocular provides three dimensional vision
C)
the binocular produces image free of chromatic aberration
D)
the binocular produces erect image
To understand why binoculars are preferred over a standard astronomical (terrestrial) telescope for watching a cricket match, we must look at the nature of the images produced: 1. Astronomical Telescopes: A basic refracting telescope produces an inverted (upside-down) image. While this is acceptable for observing stars and planets in space, it is impractical for observing terrestrial events like a sports match. 2. Binoculars: Binoculars are essentially two telescopes mounted side-by-side, but they include additional optical elements (such as prisms—Porro or Roof prisms) specifically designed to flip the image. This ensures that the final image seen by the observer is erect (upright). 3. Analysis of Options: (a) While binoculars are portable, 'ease of handling' is a secondary convenience, not the primary optical reason for their preference over a telescope for terrestrial viewing. (b) While using two eyes provides depth perception (stereopsis), the fundamental requirement for watching a match is that the players are not upside down. (c) Chromatic aberration is a property of lenses, not a distinction between binoculars and telescopes; both can suffer from it unless achromatic lenses are used. (d) The production of an erect image is the critical requirement for any terrestrial observation instrument. Therefore, the primary reason binoculars are used for a cricket match is that they produce an erect image.
Which one of the following phenomena is not explained by Huygen’s construction of wave front?
A)
Refraction
B)
Reflection
C)
Diffraction
D)
Origin of spectra
Huygens' Principle states that every point on a wavefront acts as a source of secondary spherical wavelets. This construction is used to explain the propagation of light and several optical phenomena:
1. Reflection: Explained by applying Huygens' principle to a wavefront hitting a reflecting surface, where the secondary wavelets reflect back into the medium.
2. Refraction: Explained by the change in speed of the wavefront as it passes from one medium to another, causing the wavefront to bend (Snell's Law).
3. Diffraction: Explained by the bending of light around corners, as secondary wavelets from the edge of an obstacle spread into the shadow region.
However, the 'Origin of spectra' (the emission of light of specific frequencies/colors from atoms or molecules) is a quantum mechanical phenomenon related to electronic transitions between energy levels in an atom (Bohr's model and Quantum Mechanics). Huygens' wave theory describes how light propagates once it exists, but it cannot explain how light is generated or why specific spectral lines exist.
A telescope is on the moon. If a tiny drop of ink falls on its objective, then
A)
moon will appear black
B)
field of view will be dark
C)
there will be a dark spot in the field of view
D)
brightness of the image will be slightly reduced
To understand this, we must consider how a telescope forms an image. The objective lens (or mirror) collects light from a distant object. Every point on the object sends a cone of light rays that hits the entire surface of the objective lens. All these rays are then refracted/reflected to converge at a single point in the image plane.
1. If a tiny drop of ink falls on the objective, it blocks only a small fraction of the light rays coming from every point of the observed object.
2. Since the image of any single point is formed by the integration of light from the entire aperture of the objective, blocking a small part of that aperture does not 'block' the image of a specific part of the object. Instead, it slightly reduces the total amount of light reaching the focal point for every part of the image.
3. Consequently, the entire image becomes slightly dimmer (reduced brightness), but no specific 'dark spot' appears in the field of view because the remaining clear parts of the lens still collect light from the area behind the ink drop.
Why other options are incorrect:
- Option (a): The moon is where the telescope is located; the telescope is looking at other objects, not the moon itself.
- Option (b): The field of view remains visible; it does not go completely dark unless the entire lens is covered.
- Option (c): A dark spot would only appear if the ink were placed at the focal plane (the eyepiece or the sensor), not on the objective lens. On the objective, it acts as a small stop, affecting intensity rather than geometry.
A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of the second satellite is longer than that of the first by approximately
A)
0.5%
B)
1.0%
C)
1.5%
D)
3.0%
To solve this problem, we use Kepler's Third Law of Planetary Motion, which states that the square of the orbital period (T) is proportional to the cube of the semi-major axis (R) of the orbit: T² ∝ R³. This can be written as T ∝ R^(3/2).
Let T₁ be the period of the first satellite with radius R₁, and T₂ be the period of the second satellite with radius R₂.
Given:
- R₁ = R
- R₂ = 1.01R
We want to find the fractional change in the period: (T₂ - T₁) / T₁.
Using the relationship T ∝ R^(3/2), we can use the binomial approximation for small changes. If R₂ = R₁(1 + ε), where ε = 0.01 (1%), then:
T₂ = T₁ (1 + ε)^(3/2)
According to the binomial expansion (1 + x)^n ≈ 1 + nx for |x| << 1:
T₂ ≈ T₁ (1 + (3/2)ε)
Substituting ε = 0.01:
T₂ ≈ T₁ (1 + 1.5 * 0.01)
T₂ ≈ T₁ (1 + 0.015)
Therefore, the fractional increase is:
(T₂ - T₁) / T₁ ≈ 0.015
To express this as a percentage:
0.015 * 100 = 1.5%
Comparing this to the options:
- a. 0.5% is incorrect.
- b. 1.0% is incorrect (this would be the change if T was proportional to R).
- c. 1.5% is correct.
- d. 3.0% is incorrect (this would be the change if T was proportional to R³).
Thus, the period of the second satellite is longer by approximately 1.5%.
Coriolis force is a
A)
pseudo-force that is to be added to the applied force in a rotating frame
B)
pseudo-force that is to be added to the applied force when the system is rotating
C)
force that counter-balances centrifugal force
D)
force that arises whenever there is centrifugal force
Coriolis is an inertial pseudo-force that must be added in a rotating frame; formula -2m ω×v.
Pressure applied to a gas varies inversely as volume, this is known as
A)
Charle’s law
B)
Stefan’s law
C)
Boyle’s law
D)
Kirchoff’s law
The question describes a relationship where pressure (P) varies inversely with volume (V). Mathematically, this is expressed as P ∝ 1/V, or PV = constant, provided the temperature remains constant. This is the definition of Boyle's Law.
Analysis of options:
- a. Charles's Law: States that for a fixed mass of gas at constant pressure, the volume is directly proportional to its absolute temperature (V ∝ T).
- b. Stefan's Law (Stefan-Boltzmann Law): Relates the total energy radiated per unit surface area of a black body to the fourth power of its absolute temperature (E ∝ T⁴).
- c. Boyle's Law: Correct. It defines the inverse relationship between pressure and volume at a constant temperature.
- d. Kirchhoff's Law: In thermodynamics/radiation, it states that for an arbitrary body in thermal equilibrium, emissivity equals absorptivity. In electrical circuits, it relates to current and voltage conservation.
A refrigerator is
A)
an electric motor
B)
a heat engine
C)
a heat engine working back
D)
an air cooler
A heat engine is a device that converts thermal energy (heat) from a high-temperature source into mechanical work, rejecting some heat to a low-temperature sink. A refrigerator operates on the opposite principle: it uses external mechanical work (provided by a compressor) to transfer heat from a low-temperature region (the inside of the fridge) to a high-temperature region (the surrounding room). In thermodynamics, this is described as a 'reversed heat engine' or a heat pump.
- Option (a) is incorrect because while a refrigerator contains an electric motor to drive the compressor, the refrigerator as a whole is a thermodynamic system, not a motor.
- Option (b) is incorrect because a heat engine produces work from heat, whereas a refrigerator consumes work to move heat.
- Option (d) is incorrect because an air cooler typically refers to evaporative cooling, which is a different physical process than the vapor-compression refrigeration cycle used in refrigerators.
The centre of mass of a system of particles does not depend on
A)
masses of the particles
B)
forces on the particles
C)
position of the particles
D)
relative distances between the particles
The center of mass (COM) of a system of particles is a geometric property based on the distribution of mass within the system. Mathematically, for a system of particles with masses m₁, m₂, ..., mₙ at positions r₁, r₂, ..., rₙ, the position of the center of mass (R) is given by the formula: R = (Σ mᵢrᵢ) / (Σ mᵢ).
Analyzing the options:
1. Masses of the particles (a): The formula explicitly depends on the masses (mᵢ).
2. Position of the particles (c): The formula explicitly depends on the position vectors (rᵢ).
3. Relative distances between the particles (d): Since the position of the COM depends on where the particles are located relative to an origin, it inherently depends on the relative distances between them.
4. Forces on the particles (b): The center of mass is a kinematic/geometric property. While forces determine how the center of mass *moves* (according to Newton's Second Law, F_ext = M*a_com), the *location* of the center of mass at any given instant depends only on the mass and position of the particles, not on the forces acting upon them.