Concept explainers
(a)
The mass of the core in kg and solar masses, if the core of diameter is
(a)
Answer to Problem 45Q
Solution:
Explanation of Solution
Given data:
The core of diameter is
Formula used:
Write the expression for radius.
Here,
Write the formula for volume of sphere.
Here,
Write the expression for density
Here,
Explanation:
Recall the expression for radius.
Substitute
Recall the formula for volume of sphere.
Substitute
Recall the expression for density
Substitute
Convert mass kg to solar mass.
Conclusion:
The mass of the core in kg is
(b)
The force of gravity on a 1 kg object at the surface of the core, if the core of diameter is
(b)
Answer to Problem 45Q
Solution:
Explanation of Solution
Given data:
The core of diameter is
The gravity of the mass is
Formula used:
Write the expression for the radius.
Newton’s law of gravitation for the forces between two massive body can be stated by the following equation:
Here,
Explanation:
Recall the result of part (a):
The mass of the core in kg is
Recall the expression for radius.
Substitute
Newton’s law of universal gravitation can be stated by an equation as:
Substitute
The gravitational force due to the gravity of the Earth is provided as
Conclusion:
The gravitation force due to the core of the earth is
(c)
The escape speed from the surface of the core of the star, if the diameter of the core of the star is
(c)
Answer to Problem 45Q
Solution:
Explanation of Solution
Given data:
The core of diameter is
The gravity of the mass is
Formula used:
Escape speed from Earth (
Here, G is the universal gravitational constant, m is the mass of Earth and r is the radius of Earth.
Explanation:
Recall the result of part (a):
The mass of the core in kg is
The radius is
Escape speed from Earth (
Substitute
Further solve,
The escape velocity is large, as it is half of the speed of the light. So, it can be concluded that the gases must have velocity higher than half of the velocity of the light to escape from the core surface of the star. The explosion must be much higher to attained this velocity.
Conclusion:
The speed required by a gas to escape from the surface of the star’s core in m/s is
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Chapter 20 Solutions
Universe
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