Consider a spherical cloud of gas of diameter D and density p. The only forces present in the system are pressure forces within the cloud and its self-gravity. The cloud is surrounded by empty space. For which of the following values of D is the fourth longest-wavelength mode of oscillation of the density perturbation unstable? (Below u is the speed of sound in the cloud and G is the gravitational constant) D = 3 ( D = (2) ਬ ( 5πu² Gp 2 1/2 1/2 1/2 D = D = (· πυ Gp 1/2 3пи² Gp

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Please answer within 90 minutes. State if it is Stable or Unstable.

Consider a spherical cloud of gas of
diameter D and density p. The only
forces present in the system are
pressure forces within the cloud and
its self-gravity. The cloud is
surrounded by empty space. For
which of the following values of D is
the fourth longest-wavelength mode
of oscillation of the density
perturbation unstable? (Below u is the
speed of sound in the cloud and G is
the gravitational constant)
D
= 3 (
D =
(2) ਬ
(
5πu²
Gp
2
1/2
1/2
1/2
D
=
D =
(·
πυ
Gp
1/2
3пи²
Gp
Transcribed Image Text:Consider a spherical cloud of gas of diameter D and density p. The only forces present in the system are pressure forces within the cloud and its self-gravity. The cloud is surrounded by empty space. For which of the following values of D is the fourth longest-wavelength mode of oscillation of the density perturbation unstable? (Below u is the speed of sound in the cloud and G is the gravitational constant) D = 3 ( D = (2) ਬ ( 5πu² Gp 2 1/2 1/2 1/2 D = D = (· πυ Gp 1/2 3пи² Gp
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