Question map
Consider the following statements : Statement-I : Giant stars live much longer than dwarf stars. Statement-II : Compared to dwarf stars, giant stars have a greater rate of nuclear reactions. Which one of the following is correct in respect of the above statements ?
Explanation
The correct answer is option D because Statement-I is incorrect while Statement-II is correct.
Red giants are more rare than main sequence stars, so their life spans should be shorter.[2] This directly contradicts Statement-I's claim that giant stars live much longer than dwarf stars. Main sequence stars have very long life spans[3], making dwarf (main-sequence) stars the longer-lived category.
Statement-II is correct. More massive stars are more luminous than less massive stars[4], and this higher luminosity in giant stars results from a greater rate of nuclear reactions in their cores. The increased reaction rate causes giants to burn through their fuel faster, which paradoxically shortens rather than lengthens their lifetimes compared to dwarf stars.
Therefore, Statement-I is incorrect (giants live shorter lives, not longer), but Statement-II is correct (giants do have higher nuclear reaction rates), making option D the correct choice.
SourcesPROVENANCE & STUDY PATTERN
Full viewThis is a classic 'Mechanism vs. Outcome' question. It tests the fundamental rule of stellar physics: 'Live fast, die young.' While it looks like deep astrophysics, it is solvable using the basic 'Life Cycle of a Star' charts found in standard Geography NCERTs and PMF IAS. The core logic is that high mass = high gravity = high fusion rate = short life.
This question can be broken into the following sub-statements. Tap a statement sentence to jump into its detailed analysis.
- Statement 1: In stellar evolution, do giant stars have longer lifetimes than dwarf (main-sequence) stars?
- Statement 2: In stellar physics, do giant stars have a higher nuclear fusion energy-generation rate than dwarf (main-sequence) stars?
- Statement 3: In stellar physics, does a higher nuclear fusion rate in a star cause it to have a longer stellar lifetime?
- Directly compares red giants to main-sequence stars and states giants are rarer
- Concludes rarity implies shorter life spans for giants compared to main-sequence stars
- States main-sequence stars have very long lifespans
- Implying main-sequence (dwarf) phase lasts longer than subsequent, rarer phases
- Describes main-sequence stars as living 'very long' (example: the Sun ~10 billion years)
- Explains stars leave the main sequence and swell into red giants after core hydrogen is exhausted, implying the red-giant phase follows and is shorter
States that main-sequence stars (e.g., the Sun) later swell into red giants toward the end of their life cycle, implying giants represent a later evolutionary stage rather than a longer primary lifetime.
A student could combine this with the fact that main-sequence lifetime is determined by core hydrogen burning to reason that giants are a subsequent, typically shorter-lived phase of stellar evolution.
Provides an evolutionary timeline metaphor (main sequence = 'Infancy through Adulthood'; red giant/supergiant = 'Middle Age' or 'Old Age–Death'), indicating giants occur late in life rather than having longer overall main-sequence lifetimes.
Use the timeline plus standard knowledge that massive stars evolve more rapidly to infer giants (especially supergiants) do not have longer total lifetimes than long-lived dwarfs.
Explains that red giants burn the last of their hydrogen and expand, showing the giant phase involves consuming remaining fuel in an advanced stage.
Combine with the basic idea that fuel consumption rate affects lifetime to judge whether the giant phase is shorter than a long main-sequence lifetime.
Describes massive-star endpoints (Type I/II supernovae) and violent, rapid deaths for some stars, linking high-mass (often giant) stars to relatively abrupt ends.
A student could apply the external rule that higher-mass stars burn fuel faster to connect massive/giant stars with shorter lifetimes than low-mass dwarfs.
Notes red dwarfs are common, dimmer and cooler than Sun-like stars, suggesting a class of low-mass stars distinct from giants.
Combine with the standard fact that lower luminosity/cooler stars burn fuel more slowly to hypothesize that red-dwarf (main-sequence) lifetimes exceed those of giant (high-mass) stars.
States that main-sequence stars fuse hydrogen in their cores and that stars like the Sun swell into red giants later in life (different fusion stage).
A student could combine this with the fact that different fusion fuels (H vs He) and evolutionary stage change core conditions and so affect instantaneous energy-generation rates.
Notes that when hydrogen is exhausted a star becomes a red giant and begins fusing helium, and that more massive stars undergo further, higher-stage nuclear burning.
Using the basic idea that higher fusion stages (and higher-mass stars) require and produce different energy outputs, a student can suspect massive/advanced-burning stars may have higher fusion power than low-mass main-sequence stars.
Says red dwarfs are common and are substantially dimmer and cooler than stars like the Sun.
A student could use the luminosity clue (dimmer red dwarfs) plus a mass–luminosity expectation to infer lower fusion rates in low-mass main-sequence stars compared with brighter stars.
Explains fusion produces outward pressure balanced by gravity and that loss of fusion causes gravitational collapse to degenerate states—linking fusion rate to core pressure/temperature and thus to mass/density.
Combining this with the basic fact that core temperature/pressure scale with mass, a student can reason that more massive cores enable higher fusion rates.
States fusion requires far more pressure and temperature than found in Earth, implying that mass (and resulting pressure/temperature) is crucial for fusion.
A student could extend this to compare stellar masses: stars with greater core pressure/temperature (often more massive or in advanced phases) are likely to have higher fusion-generation rates than low-mass stars.
- States that fusion in the core uses hydrogen as fuel and that when hydrogen vanishes fusion slows and the star collapses.
- Implies that consuming the hydrogen fuel determines the end of the star’s active fusion phase, so faster consumption would shorten the available fuel supply.
- Defines fusion as conversion of hydrogen to helium with release of large amounts of energy, indicating hydrogen is the consumable fuel.
- Identifies the high temperatures required for fusion, linking fusion activity to conditions that govern fuel burn.
- [THE VERDICT]: Conceptual Sitter. Solvable by applying the basic 'Mass-Luminosity Relation' taught in Physical Geography (Chapter: The Universe).
- [THE CONCEPTUAL TRIGGER]: Stellar Evolution. Specifically, the transition from 'Main Sequence' (Dwarfs) to 'Red Giant' and the trade-off between fuel consumption and longevity.
- [THE HORIZONTAL EXPANSION]: Memorize these stellar limits: 1. Chandrasekhar Limit (1.44 solar masses - White Dwarf cutoff). 2. Oppenheimer-Volkoff Limit (Neutron Star cutoff). 3. H-R Diagram positions (Sun = Main Sequence; Giants = Top Right). 4. Color-Temp rule (Blue = Hot/Young, Red = Cool/Old).
- [THE STRATEGIC METACOGNITION]: Do not just memorize the stages (Protostar -> Red Giant). Understand the *engine*. Ask: 'What fights gravity?' (Fusion pressure). 'What happens when fuel runs out?' (Collapse). If you understand the engine, you know that a bigger engine burns fuel faster.
Main‑sequence stars fuse hydrogen in their cores and make up about 90% of stars, marking the principal, long‑lasting phase of a star's life.
High‑yield: Explains why most observed stars are on the main sequence and underpins direct comparisons of stellar lifetimes; links to nuclear fusion, stellar structure and habitability, and helps answer questions about which evolutionary phase is longest or most common.
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Main sequence stars > p. 10
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > 1.5. Star Formation (Stellar Evolution or Life Cycle of a Star) > p. 9
Stars like the Sun expand into red giants toward the end of their lives, burning their remaining fuel and representing a later evolutionary (older) stage after the main sequence.
High‑yield: Clarifies the sequence from main sequence to giant to remnant stages, connects to planetary nebula and white dwarf formation, and helps in questions asking about ordering of stellar life phases or causes of stellar expansion.
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Main sequence stars > p. 10
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Red Supergiant > p. 11
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Neutron stars > p. 14
A star's mass determines whether it ends as a white dwarf, neutron star, or black hole, which in turn relates to different evolutionary tracks and timescales.
High‑yield: Mass‑dependence explains why lifetimes and end states vary across stars, links to supernova mechanisms and remnant types, and enables answering questions on why massive and low‑mass stars evolve differently.
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Neutron stars > p. 14
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Black holes > p. 15
Main-sequence stars generate their energy by fusing hydrogen into helium in their cores.
High-yield for questions on stellar classification and energy production; connects to stellar lifetimes, luminosity and the Sun as an example. Mastering this lets aspirants compare energy sources and states of different stellar classes in conceptual questions.
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Main sequence stars > p. 10
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > 1.5. Star Formation (Stellar Evolution or Life Cycle of a Star) > p. 9
Red giants burn helium and, in more massive stars, progress to fuse heavier elements such as carbon during later evolutionary stages.
Important for questions on stellar evolution and nucleosynthesis; links to element formation, life-cycle endpoints (planetary nebula, supernova) and observational properties of evolved stars. Understanding this clarifies why stellar behavior and outputs change with age and mass.
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Importance of Supernova: Creating and Dispersing New Elements > p. 14
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Main sequence stars > p. 10
A star's outward pressure from fusion balances inward gravity; when fusion wanes the star can collapse into degenerate matter or ignite runaway fusion in compact remnants.
Crucial for questions on stellar stability, end-states (white dwarf, supernova) and related energetic events; links core processes to eventual outcomes and observational phenomena like novae/supernovae. Useful for reasoning about energy budgets and structural changes.
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Degenerate Matter > p. 11
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Type I supernova or Type Ia supernova (read as one-a) > p. 12
A star’s active life ends when its hydrogen fuel is exhausted, so the rate of fuel consumption sets the duration of its fusion-powered phase.
High-yield for questions on stellar evolution and life cycles; links star mass, fusion activity, and end states (white dwarf, neutron star, black hole). Enables reasoning-based answers about why massive stars have shorter main-sequence lifetimes despite higher luminosity.
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Degenerate Matter > p. 11
- Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Protostar > p. 9
The Hertzsprung-Russell (H-R) Diagram. Since they asked about Giants vs. Dwarfs, the next logical question is about their Temperature vs. Luminosity. Expect a statement like: 'Red Giants are cooler than the Sun but brighter due to their size.'
The 'Bonfire vs. Candle' Logic. A giant bonfire (Giant Star) releases heat (reaction rate) much faster than a small candle (Dwarf Star). Common sense dictates that the one burning furiously runs out of fuel quicker. Therefore, if Statement II (greater reaction rate) is true, Statement I (lives longer) MUST be false. They are inversely proportional.
Energy Security (Mains GS-3). The fusion process in stars (Hydrogen to Helium) is exactly what terrestrial projects like ITER (International Thermonuclear Experimental Reactor) attempt to replicate. The 'high gravity' of stars is replaced by 'magnetic confinement' in Tokamaks.