Question

Define gravitational potential energy and derive an expression for it associated with two particles of masses m₁ and m₂.

Answer 1

Gravitational potential energy is the energy possessed by an object because of its position in the gravitational field. As you know gravitational force is attractive in nature so, gravitational potential energy always be negative.

e.g., $W=-\int\limits^r_{\infty}{F}\,dr$

As you know, force , $F=\frac{Gm_1m_2}{r^2}$ [ from Newton's law of Gravitation ]

So, $W=-Gm_1m_2\left[\frac{-1}{r}\right]^r_{\infty}$

Or, $W=\frac{Gm_1m_2}{r}$

As we know, potential energy = - workdone.

Hence, gravitational potential energy = -W = $-\frac{Gm_1m_2}{r}$

Here, G is gravitational constant and r is the separation between masses.

Answer 2

Answer:

Gravitational potential energy is the energy possessed by an object because of its position in the gravitational field. As you know gravitational force is attractive in nature so, gravitational potential energy always be negative.

e.g., W=-\int\limits^r_{\infty}{F}\,drW=−

∞

∫

r

Fdr

As you know, force , F=\frac{Gm_1m_2}{r^2}F=

r

2

Gm

1

m

2

[ from Newton's law of Gravitation ]

So, W=-Gm_1m_2\left[\frac{-1}{r}\right]^r_{\infty}W=−Gm

1

m

2

[

r

−1

]

∞

r

Or, W=\frac{Gm_1m_2}{r}W=

r

Gm

1

m

2

As we know, potential energy = - workdone.

Hence, gravitational potential energy = -W = -\frac{Gm_1m_2}{r}−

r

Gm

1

m

2

Here, G is gravitational constant and r is the separation between masses.