How bright a star appears from Earth is the star's apparent magnitude.
Answer:
The gravitational potential energy of a system is -3/2 (GmE)(m)/RE
Explanation:
Given
mE = Mass of Earth
RE = Radius of Earth
G = Gravitational Constant
Let p = The mass density of the earth is
p = M/(4/3πRE³)
p = 3M/4πRE³
Taking for instance,a very thin spherical shell in the earth;
Let r = radius
dr = thickness
Its volume is given by;
dV = 4πr²dr
Since mass = density* volume;
It's mass would be
dm = p * 4πr²dr
The gravitational potential at the center due would equal;
dV = -Gdm/r
Substitute (p * 4πr²dr) for dm
dV = -G(p * 4πr²dr)/r
dV = -G(p * 4πrdr)
The gravitational potential at the center of the earth would equal;
V = ∫dV
V = ∫ -G(p * 4πrdr) {RE,0}
V = -4πGp∫rdr {RE,0}
V = -4πGp (r²/2) {RE,0}
V = -4πGp{RE²/2)
V = -4Gπ * 3M/4πRE³ * RE²/2
V = -3/2 GmE/RE
The gravitational potential energy of the system of the earth and the brick at the center equals
U = Vm
U = -3/2 GmE/RE * m
U = -3/2 (GmE)(m)/RE
Answer:
Explanation:
a )
In space due to weightlessness both astronaut and her oxygen tank will float .
when she throws the tank away from spacecraft , she will have a velocity in opposite direction ie towards the spacecraft . This happens due to conservation of momentum . She creates a momentum away so that she can get a momentum towards the spaceship.
So
m₁ v₁ = m₂v₂
12 x 8 = ( 87 - 12 ) x v₂
v₂ = 1.28 m /s
Time allowed = 2 x 60
= 120 s
So maximum distance upto which she can remain away from spacecraft
= 120 x 1.28
= 153 m .
b )
The Newton's law which explains the theory behind it is "third law of motion" . This law gives law of conservation of momentum .
Mechanical energy is conserved when there are no non-conservative forces acting on the body. Examples are friction and elastic forces of stress in a body. These non-conservative forces convert mechanical energy to other forms of energy like heat and sound
Hope this makes sense
