Two bodies A and B having masses 2 kg and 4 kg respectively are separated by 2 m. Where should a body of mass 1 kg be placed so that the gravitational force on this body due to bodies A and B is zero?

Answer

`0.83m`

Explanation

Here, mass of body `A, m_(1)=2 kg` , mass of body `B, m_(2)=4 kg`
distance between the bodies A and `B =2m`
mass of body `C, m=1 kg`
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 `(Gm_(1)m)/x^(2)=(Gm_(2)m)/(2-x)^(2)` or `m_(1)/x^(2)=m_(2)/(2-x)^(2)`
or `2/ x^(2)=4/(2-x)^(2) or 2x^(2)=(2-x)^(2)`
Taking square root of both sides, we get `sqrt2x=2-x`
or `1.414x+x=2 or x=2/2.414=0.83m`