the figure(figure 1) shows a particle of mass m at distance x along the axis of a very thin ring of mass m and radius r. calculate the gravitational potential energy of these two masses. use what you know about the relationship between force and potential energy to find the magnitude of the gravitational force on m when it is at position x>0 .

Potential energy is accumulated as a result of the work required to displace a mass (m) from infinity to a position inside the gravitational field of a source mass (M) without accelerating it. These are referred to as gravitational potential energies. The sign Ug is used to denote it.

We are aware that a body's stored energy in a certain position is what is meant by the term potential energy of a body. The change in potential energy is equal to the amount of work done on the body by the applied external forces if the body's position changes as a result of the application of those forces.

Let's break the disc into small rings

dm− mass of the ring,

So. dm=2πrdr× M

πr²

So, potential dP= −Gdm

√(x² +r²)

So, dP= G.2πxtanϕxsec 2 ϕdϕ

(x√( 1+tan 2 ϕ )) πr²

⇒P= −2GMx ∫ tan (R/x) tanϕsecϕdϕ

r²

⇒P= −2GMx {1− 1 }

r² cos(tan 2 (R/x))

⇒P= -2GM((√r²+x²)-x)

r²

Hence, gravitational potential energy of these two masses is -2GM((√r²+x²)-x)

r²

To know more about gravitational potential energy from the given link

https://brainly.com/question/3120930

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