Question

a body of mass 1kg is placed at a distance of 2m from another body of mass 10kg .at what distance from the body of mass 1kg another body of mass 5kg be placed so that the net force of gravitation acting on the body 1kg is 0

Answer 1

use concept of neutral point.

Answer 2

Answer:

x=1.414 m where the net gravitational force on the mass of 1 kg will be zero.

Explanation:

The mass of the first body is $m_{1}=1\ kg$

The mass of the second body is $m_{2}=10\ kg$ which is right of the first mass

The distance between both the bodies is d=2 m

The third mass $m_{3}=5\ kg$ is placed at distance x from the first mass $m_{1}$ which is left of the first mass.

The gravitational force between the first mass and the second mass is

$F_{1}=\dfrac{Gm_{1} m_{3}}{x^2}$

The direction is towards right of the first mass

The gravitational force between the first mass and the second mass is,

$F_{2}=$

The direction is towards left of the first mass.

We know that net gravitational force on the first mass is zero

$F_{1}=F_{2}\\\dfrac{Gm_{1} m_{3}}{x^2}=\dfrac{Gm_{1}m_{2}}{d^2}\\\dfrac{1\times 5}{x^2}=\dfrac{1\times 10}{2^2}\\5\times 4=10 x^2\\x^2=\dfrac{20}{10}\\x^2=2\\x=\sqrt{2}=1.414\ m$