Two masses each of 2kg and 4kg are placed at a distance of 2m from each other .A third mass of 1kg is placed midway between these masses what is net gravitational force on 1kg mass?
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Answer:
Here, mass of body A,m
1
=2kg, mass of body B,m
2
=4kg
distance between the bodies A and B=2m
mass of body C,m=1kg
Let body C be placed at a distance x from A,
Thus, AC=x and BC=(2−x)
As gravitational force on C due to A= gravitational force on C due to B,
F
1
=F
2
or
x
2
Gm
1
m
=
(2−x)
2
Gm
2
m
or
x
2
m
1
=
(2−x)
2
m
2
or
x
2
2
=
(2−x)
2
4
or2x
2
=(2−x)
2
Taking square root of both sides, we get
2x
=2−x
or 1.414x+x=2orx=
2.414
2
=0.83m
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