Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsGravitation4 Marks
Question
Explain the relation between the gravitational potential energy and the gravitational potential.
✓
Answer
$1.$ In terms of potential, we can write the potential energy of the Earth$-$mass system as, Gravitational potential energy $(U) =$ Gravitational potential $(V_r) \times$ mass $(m)$
$2.$Thus, gravitational potential is gravitational potential energy per unit mass.
$\therefore V _{ r }=\frac{ U }{ m }$
$3.$For any conservative force field, the concept of potential can be defined on similar lines.
$4.$Gravitational potential difference between any two points in gravitational field can be written as,
$ V _2- V _1=\frac{U_2-U_1}{m}$
$=\frac{ dW }{ m }$
This is the work done $($or change in potential energy$)$ per unit mass.
$5.$Therefore, in general, for a system of any two masses $m_1$ and $m_2,$ separated by distance $r,$ we can write,
$U=-\frac{G m_1 m_2}{r}$
$=\left(V_1\right) m_2$
$=\left(V_2\right) m_1$
Here $V_1$ and $V_2$ are gravitational potentials at $r$ due to $m_1$ and $m_2$ respectively.
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