Answer:


Explanation:
Given:
Let mass of the particle B be, 
then the mass of particle A, 
Energy stored in the compressed spring, 
Now when the compression of the particles with the spring is released, the spring potential energy must get converted into the kinetic energy of the particles and their momentum must be conserved.
Kinetic energy:

.............................(1)
<u>Using the conservation of linear momentum:</u>

.............................(2)
Put the value of
from eq. (2) into eq. (1)

...........................(3)
<u>Now the kinetic energy of particle B:</u>



Put the value of
form eq. (3) into eq. (1):

<u>Now the kinetic energy of particle A:</u>
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The nucleus is the core of an atom which is made up of protons and neutrons. Every single type of atom has a dense center and the majority of the mass is located in here.
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