UPSC Geoscientist

11. The refractive index of a prism made of flint glass is

The refractive index of a prism made of flint glass is

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the same for all wavelengths in white light
higher for red light than for violet light
higher for violet light than for red light
highest for green and yellow lights and lowest for violet and red lights
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The refractive index of a material varies with the wavelength of light. For most transparent materials, including flint glass, the refractive index is higher for shorter wavelengths (like violet light) than for longer wavelengths (like red light). This phenomenon is known as dispersion.
– Shorter wavelengths are bent more than longer wavelengths when passing through a prism. This is why white light is dispersed into its constituent colours.
– Higher refractive index means light bends more, which corresponds to shorter wavelengths (violet end of the spectrum).
– Lower refractive index means light bends less, which corresponds to longer wavelengths (red end of the spectrum).
The relationship between refractive index (n) and wavelength (λ) is described by Cauchy’s equation, which states that for a given material, n is approximately proportional to A + B/λ², where A and B are constants. As wavelength (λ) increases, the refractive index (n) decreases. Violet light has a shorter wavelength than red light.

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12. Which one of the following colours of the visible spectrum of light is

Which one of the following colours of the visible spectrum of light is least absorbed by the green plants?

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Violet
Red
Green
Yellow
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Green plants appear green because they reflect or transmit green light rather than absorbing it significantly for photosynthesis.
– Photosynthesis primarily utilizes light from the blue and red ends of the visible spectrum, as chlorophyll pigments absorb these wavelengths most effectively.
– Green light is poorly absorbed by chlorophyll, hence it is reflected or transmitted, making the plants appear green.
The absorption spectrum of chlorophyll a and chlorophyll b shows peaks in the blue-violet and red regions, with a dip in the green region. While some green light is absorbed by accessory pigments like carotenoids, the overall absorption is lowest for green light compared to other colours essential for photosynthesis.

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13. Which one of the following greenhouse gases is man-made?

Which one of the following greenhouse gases is man-made?

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Carbon dioxide
Chlorofluorocarbon
Methane
Nitrous oxide
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Chlorofluorocarbons (CFCs) are entirely synthetic, man-made chemicals. They do not have significant natural sources and were developed for various industrial applications such as refrigerants, aerosols, and cleaning solvents. They are potent greenhouse gases.
Greenhouse gases trap heat in the Earth’s atmosphere, contributing to the greenhouse effect. While carbon dioxide, methane, and nitrous oxide are naturally occurring gases, their atmospheric concentrations have been significantly increased by human activities (anthropogenic emissions). In contrast, CFCs are purely anthropogenic compounds.
CFCs were widely used but are now largely phased out under international agreements (like the Montreal Protocol) because they also contribute to the depletion of the stratospheric ozone layer, in addition to being powerful greenhouse gases. Other exclusively man-made greenhouse gases include Hydrofluorocarbons (HFCs), Perfluorocarbons (PFCs), and Sulphur Hexafluoride (SF₆).

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14. With reference to the electron drift speed in a current-carrying condu

With reference to the electron drift speed in a current-carrying conductor, which one of the following statements is correct?

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It is much more than the average electron speed.
It is much lesser than the average electron speed.
It is very close to the average electron speed.
It is close to the speed of light.
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The average speed of electrons due to their random thermal motion in a conductor at room temperature is very high (on the order of 10⁵ to 10⁶ m/s). When a voltage is applied, the electrons acquire a net drift velocity in the direction opposite to the electric field. This drift speed is typically very low, on the order of millimeters per second (10⁻⁴ to 10⁻³ m/s), much less than their random thermal speed.
In the absence of an electric field, free electrons in a conductor move randomly due to thermal energy, colliding with lattice ions. Their average velocity is zero, but their average speed is high. When an electric field is applied, the electrons experience a force that causes them to accelerate between collisions. Although collisions are frequent, resulting in a zig-zag path, there is a net average velocity in the direction of the force, which is the drift velocity. This drift velocity is responsible for the electric current.
The speed of the electrical signal or current propagation (which is essentially the speed of the electromagnetic field driving the electrons) is very close to the speed of light in the conductor, but this is distinct from the physical drift speed of the individual charge carriers (electrons).

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15. The derivation of Bernoulli’s equation for fluid flow takes certain as

The derivation of Bernoulli’s equation for fluid flow takes certain assumptions. Which one of the following assumptions is not among them?

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Gravitational forces can be neglected
Turbulence of fluid flow can be neglected
Viscous forces can be neglected
Frictional forces can be neglected
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Bernoulli’s equation includes a term (gh or ρgh) that specifically accounts for the effect of gravity on the fluid’s potential energy. Therefore, the assumption that gravitational forces can be neglected is incorrect; rather, gravity is included in the derivation.
Bernoulli’s equation is derived from the application of the conservation of energy principle to fluid flow under specific idealizing assumptions. These assumptions typically include that the fluid is incompressible, the flow is steady, inviscid (no viscous forces or internal friction), and often irrotational (negligible turbulence). The derivation considers the work done by pressure forces and gravity on a fluid element as it moves along a streamline, relating changes in pressure, velocity, and height (potential energy due to gravity).
The standard form of Bernoulli’s equation along a streamline is P + ½ρv² + ρgh = constant, where P is pressure, ρ is density, v is velocity, g is acceleration due to gravity, and h is height. The term ρgh represents the potential energy per unit volume of the fluid due to gravity. Neglecting viscous and frictional forces simplifies the energy balance by assuming no energy is lost to internal friction or dissipation. Neglecting turbulence assumes the flow is smooth and ordered (laminar or irrotational).

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16. Which one of the following is the conservation law from which the equa

Which one of the following is the conservation law from which the equation of continuity for fluid flow is derived?

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Conservation of momentum
Conservation of volume
Conservation of mass
Conservation of energy
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The equation of continuity for fluid flow is a direct consequence of the conservation of mass principle. It states that mass is conserved within a flowing fluid system, meaning it is neither created nor destroyed.
In a steady flow of a fluid, the equation of continuity relates the fluid density, flow speed, and cross-sectional area of the flow channel. For any given section of a fluid flow, the rate at which mass enters that section must equal the rate at which mass leaves, assuming no sources or sinks within the section. This principle is a statement of mass conservation applied to fluid dynamics.
For an incompressible fluid (where density ρ is constant), the continuity equation simplifies to A₁v₁ = A₂v₂, meaning the product of the cross-sectional area and the fluid velocity is constant along a streamline. This reflects that if the area decreases, the velocity must increase to maintain a constant mass flow rate. Other conservation laws (momentum and energy) are fundamental to deriving other equations in fluid dynamics, such as the Navier-Stokes equations and Bernoulli’s equation, respectively.

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17. On a very hot day, we often see shimmering wavy lines near the ground.

On a very hot day, we often see shimmering wavy lines near the ground. It is due to

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dispersion of light
refraction of light
reflection of light
total internal reflection of light
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The shimmering wavy lines observed near the ground on a hot day are caused by the refraction of light as it passes through layers of air with varying temperatures and densities, leading to variations in the refractive index.
On hot days, the ground heats the air just above it, creating a significant temperature gradient. Hot air is less dense than cooler air and has a slightly lower refractive index. Light rays passing through these layers of air with different refractive indices are continuously bent (refracted). As convection causes these pockets of hot and cool air to move and mix, the light rays are constantly being bent in different directions, making distant objects appear distorted, blurred, and wavy or shimmering. This is a form of atmospheric refraction.
This phenomenon is closely related to the formation of mirages, which are more pronounced examples of atmospheric refraction occurring when light is strongly bent as it passes from cooler, denser air into warmer, less dense air near a hot surface. The shimmering effect is a less extreme, constantly changing manifestation of the same principle of refraction due to thermal gradients in the atmosphere.

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18. The appearance of a rainbow in the sky after a rain shower is due to

The appearance of a rainbow in the sky after a rain shower is due to

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diffraction and refraction of light in water droplets
total internal reflection of light in water droplets only
refraction of light in water droplets only
both total internal reflection and refraction of light in water droplets
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The formation of a rainbow is due to the combined effects of refraction and total internal reflection (or simply internal reflection) of sunlight as it passes through spherical rain droplets.
When sunlight enters a rain droplet, it is refracted (bends) and dispersed (separated into different colors because different wavelengths refract at slightly different angles). This dispersed light then travels to the back inner surface of the droplet, where it undergoes internal reflection. Finally, as the light exits the droplet, it is refracted again, further separating the colors and sending them towards the observer’s eye at specific angles depending on the wavelength, creating the arc of the rainbow. For the primary rainbow, the reflection at the back surface is usually total internal reflection, but even if not strictly TIR for all angles, it is an internal reflection that directs the light back towards the observer.
A double rainbow occurs due to light undergoing two internal reflections within the droplet. Diffraction effects can lead to phenomena like supernumerary bows, which are faint bands seen just inside the primary rainbow, but the primary and secondary rainbows themselves are primarily explained by the principles of refraction and internal reflection.

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19. Which one of the following statements is true about the appearance of

Which one of the following statements is true about the appearance of colour of the Sun in the sky?

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At sunset (or sunrise), sunlight travels more distance in the atmosphere and higher frequency radiations scatter away resulting into red sunset (or sunrise).
At sunset (or sunrise), sunlight travels least distance in the atmosphere and higher frequency radiations scatter away resulting into red sunset (or sunrise).
At noon, sunlight travels least distance in the atmosphere and relatively less amount of sunlight is scattered and therefore the Sun appears reddish.
At noon, sunlight travels least distance in the atmosphere and larger amount of sunlight is scattered and therefore the Sun appears reddish.
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At sunset or sunrise, sunlight travels a longer path through the Earth’s atmosphere. This longer path means more scattering of sunlight occurs. According to Rayleigh scattering, shorter wavelengths (blue and violet light) are scattered much more effectively than longer wavelengths (red and orange light). As the blue and violet light is scattered away from the line of sight, the light that reaches the observer’s eyes is richer in longer wavelengths, making the Sun appear reddish.
The color of the sky and the Sun’s appearance depend on how sunlight is scattered by molecules in the atmosphere. Rayleigh scattering dictates that scattering is inversely proportional to the fourth power of the wavelength (scattering ∝ 1/λ⁴). This means shorter wavelengths scatter significantly more than longer ones. The path length of sunlight through the atmosphere is the key factor explaining the difference between the Sun’s appearance at noon (shortest path, less scattering) and at sunrise/sunset (longest path, more scattering of short wavelengths).
At noon, when the Sun is high in the sky, the path through the atmosphere is shortest. Less scattering occurs, and although blue light is still scattered away (making the sky blue), enough of the other wavelengths remain in the direct beam that the Sun appears white or slightly yellow.

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20. The characteristics of gravitational waves that make them difficult to

The characteristics of gravitational waves that make them difficult to detect are

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long wavelength and high energy
long wavelength and low energy
short wavelength and high energy
short wavelength and low energy
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Gravitational waves are difficult to detect primarily because they interact very weakly with matter, resulting in incredibly small amplitudes (strains) by the time they reach detectors on Earth. This weak interaction is associated with low energy flux at large distances from the source. The relevant wavelengths for detectable sources are often quite long (hundreds to thousands of kilometers for ground-based detectors, much longer for proposed space-based detectors), which necessitates very large and sensitive instruments like interferometers.
The difficulty in detecting gravitational waves stems from their weak coupling to matter. This means they cause only tiny distortions (strains) in spacetime as they pass through. Even waves from catastrophic events like black hole mergers result in strains of only about 10⁻²¹ to 10⁻²². Detecting such minuscule changes requires extraordinarily sensitive instruments, isolated from environmental noise. The energy carried by the waves, while immense near the source, spreads out over vast cosmic distances, leading to extremely low energy flux at the detector.
Ground-based detectors like LIGO and Virgo use interferometry to measure these minute changes in length caused by a passing gravitational wave. Future space-based detectors like LISA are designed to detect lower-frequency gravitational waves with much longer wavelengths, originating from different types of sources. The “long wavelength and low energy (flux at detection)” combination accurately reflects the challenges in detecting these elusive ripples in spacetime.

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