Question

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

Answer 1

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

=

Answer 2

Explanation:

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