Two point mass m1 and m2 distance r apart find gravitational potential where gravitational intensity zero
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Answer:
Suppose the two bodies (A and B) of masses m
1
and m
2
produces zero. Zero resultant gravitational field at C where AC=x So BC=R−x
Therefore,
x
2
GM
1
=
(R−x)
2
GM
2
or, (R−x)
M
1
=x
M
2
or, x=
M
1
+
M
2
R
M
1
and R−x=R−[
M
1
+
M
2
R
M
1
]=
M
1
+
M
2
R
M
2
So,
x
1
=
R
M
1
M
1
+
M
2
and
R−x
1
=
R
M
2
M
1
+
M
2
Now Gravitational Potential is given by
=
x
−GM
1
+[
(R−x)
−GM
2
]
=−G[
x
M
1
+
R−x
M
2
]
Putting Values from above:
Gravitational Potential =−G[M
1
R
M
1
M
1
+
M
2
+M
2
R
M
2
M
1
+
M
2
]
V=
R
−G
[M
1
+M
2
+2
M
1
M
2
]
x=−(
M
1
+
M
2
)
2
R
G
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