a) A star population in a galaxy is composed of stars with masses in the range 1M - 75M. The initial mass function of the population is (M) = (M/M)-2.3, where p = (MO). = 109 M¹ find the total number of stars in the population. Knowing that b) Consider the surface density wave 01 = 010e (wt-10+ar 4/3) " where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi- nate. w is the angular frequency (w > 0), a is a positive constant, and σ10 is the amplitude of the wave. 1. Using mathematical arguments show whether the pattern described by σ₁ is rotating clockwise or anticlockwise. c) 2. Using mathematical arguments show how the distance between wavefronts depends on r. Specify whether it increases or decreases with r. Determine how many arms the spiral has. Consider a spherical cloud of mass M and radius R. The density profile in its interior has the form p(r) = A/r, where r is the radial coordinate from the centre of the cloud and A is a constant. Prove that its total gravitational energy, 2, has the form: GM² Ω = -γ R where G the gravitational constant and is a real number. Find y.
a) A star population in a galaxy is composed of stars with masses in the range 1M - 75M. The initial mass function of the population is (M) = (M/M)-2.3, where p = (MO). = 109 M¹ find the total number of stars in the population. Knowing that b) Consider the surface density wave 01 = 010e (wt-10+ar 4/3) " where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi- nate. w is the angular frequency (w > 0), a is a positive constant, and σ10 is the amplitude of the wave. 1. Using mathematical arguments show whether the pattern described by σ₁ is rotating clockwise or anticlockwise. c) 2. Using mathematical arguments show how the distance between wavefronts depends on r. Specify whether it increases or decreases with r. Determine how many arms the spiral has. Consider a spherical cloud of mass M and radius R. The density profile in its interior has the form p(r) = A/r, where r is the radial coordinate from the centre of the cloud and A is a constant. Prove that its total gravitational energy, 2, has the form: GM² Ω = -γ R where G the gravitational constant and is a real number. Find y.
College Physics
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ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:a) A star population in a galaxy is composed of stars with masses in the range 1M - 75M.
The initial mass function of the population is (M) = (M/M)-2.3, where p = (MO).
= 109 M¹ find the total number of stars in the population.
Knowing that
b) Consider the surface density wave
01 = 010e (wt-10+ar 4/3)
"
where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi-
nate. w is the angular frequency (w > 0), a is a positive constant, and σ10 is the amplitude
of the wave.
1. Using mathematical arguments show whether the pattern described by σ₁ is rotating
clockwise or anticlockwise.
c)
2. Using mathematical arguments show how the distance between wavefronts depends
on r. Specify whether it increases or decreases with r. Determine how many arms
the spiral has.
Consider a spherical cloud of mass M and radius R. The density profile in its interior has
the form p(r) = A/r, where r is the radial coordinate from the centre of the cloud and A is
a constant. Prove that its total gravitational energy, 2, has the form:
GM²
Ω = -γ
R
where G the gravitational constant and is a real number. Find y.
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