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
Guest previewThis 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.
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