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?
(a). Both Statement-I and Statement-II
are correct and Statement-II explains Statement-I
(b). Both Statement-I and Statement-II
are correct, but Statement-II does not explain Statement-I
(c). Statement-I is correct, but
Statement-II is incorrect
(d). Statement-I is incorrect, but
Statement-II is correct
Explanation:
Statement I is incorrect because giant
stars actually have shorter lifespans than dwarf stars due to their faster rate
of nuclear reactions. Statement II is correct as giant stars have a greater
rate of nuclear reactions compared to dwarf stars.
Statement II is correct: giant stars have
a faster rate of nuclear reactions than dwarf stars. However, this means that
giant stars actually have shorter lifespans than dwarf stars because they use
up their hydrogen fuel faster.
Giant stars are more massive than dwarf stars, and their greater mass causes them to compress gas more. This gas pressure resists compression, but it's not enough to prevent the star from collapsing due to gravity. When the core temperature reaches about 10 million K, hydrogen fusion occurs, releasing energy that creates radiation pressure. This radiation pressure, combined with the gas pressure, balances the inward pull of gravity and prevents further collapse.
Giant stars also have a larger radius and
luminosity than main-sequence stars with the same surface temperature. They can
have radii up to a few hundred times that of the Sun, and luminosities between
10 and a few thousand times that of the Sun.
Therefore, the correct option is (d).