Question

two bodies of 10kg and 1000kg are at a distance 1m apart .At which point on the line joining them will the gravitational field intensity is zero

Answer 1

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Solution:
(1st method)
m1=100kg
m2=1000kg
r=1m

Let x be the distance of point P from 100kg where the resultant gravitational Intensity is zero.

Gravitational Intensity at P due to body of mass 100kg is equal and opposite to that of object of mass 10,000kg

Gx100/x²=Gx10000/(1-x)²

(1-x)²=100x²

10x =1-x

11x=1

x=1/11m

Therefore at this point gravitational field intensity will be zero.


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(2 method)
Let at x distance from m₁ and 1 -x distance from m₂ Gravitational field intensity will be zero. 

we know, 
Magnitude Gravitational field intensity = GM/R² 

Here, 
m₁ = 10 Kg , m₂ = 1000 Kg 
A/C to question, 
Gm₁/x² = Gm₂/(1 - x)² 
10/x² =1000/(1 - x)² 
1/x²= 100/(1 - x)² 
1/x = 10/(1 - x) 
1 - x = 10x 
1 = 11x ⇒ x = 1/11 m 

Hence, from m₁ distance will be 1/11 m 
And from m₂ , distance will be 10/11 m



Both are same.

Answer 2

Attachment is given here