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Two bodies of mass m1 amd m2 are separated by a distance x.What is the gravitational potential at the point where gravitational field is zero?

Two bodies of mass m1 amd m2 are separated by a distance x.What is the gravitational potential at the point where gravitational field is zero?

Grade:11

2 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Let the distance of that point fromm_1ber.

Since gravitational field at that point is zero,

\dfrac{Gm_1}{r^2}=\dfrac{Gm_2}{(x-r)^2}
\implies \dfrac{r}{x-r}=\sqrt{\dfrac{m_1}{m_2}}
\implies r=(\dfrac{\sqrt{m_1}}{\sqrt{m_1}+\sqrt{m_2}})x

The gravitational potential at this point is-\dfrac{Gm_1}{r}-\dfrac{Gm_2}{x-r}=-\dfrac{G}{x}(\sqrt{m_1}+\sqrt{m_2})^2
Gitanjali Rout
184 Points
5 years ago
-\dfrac{Gm_1}{r}-\dfrac{Gm_2}{x-r}=-\dfrac{G}{x}(\sqrt{m_1}+\sqrt{m_2})^2The gravitational potential at this point is\implies r=(\dfrac{\sqrt{m_1}}{\sqrt{m_1}+\sqrt{m_2}})x\implies \dfrac{r}{x-r}=\sqrt{\dfrac{m_1}{m_2}}\dfrac{Gm_1}{r^2}=\dfrac{Gm_2}{(x-r)^2}.Since gravitational field at that point is zero,rbem_1Let the distance of that point from
 
thanks

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