
Concept explainers
(a)
The average density of a
Earth.
(a)

Answer to Problem 30Q
Explanation of Solution
Given data:
The mass of the star is
Formula used:
The average density of the star can be calculated by using the following relation:
Here,
Write the expression for the volume of a sphere.
Here,
Explanation:
Since the mass of the star is given in solar mass, convert it into standard the mass unit, that is, kilograms.
Recall the expression for the volume of a sphere.
Substitute
Recall the expression for the average density of a star.
Substitute
Conclusion:
The average density of the dwarf star,
(b)
Whether or not the star’s density is the same as the density of about an elephant per teaspoon, along with proper calculation.
(b)

Answer to Problem 30Q
No, the star’s density is approximately twice that of about an elephant per teaspoon.
Explanation of Solution
Given data:
Let us consider a general elephant with mass 4000 kg and an ordinary teaspoon with volume
Formula used:
Write the expression of the density as -
Here,
Explanation:
The density will be calculated as:
Substitute
Compare
Conclusion:
The density of the dwarf star is approximately twice that of about an elephant per teaspoon. So, the provided statement is incorrect.
(c)
The escape speed required for a gas to eject from the star’s surface.
(c)

Answer to Problem 30Q
Explanation of Solution
Given data:
The mass of the star is
Formula used:
Write the expression for escape speed.
Here,
Explanation:
The escape speed is the minimum speed required to send an object out of the gravitational field of the body it is being sent from.
Recall the expression for escape speed.
Substitute
Conclusion:
The escape speed for the gas is
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