Question

Two bodies of masses 10 kg and 1000 kg are at distance 1 m apart. At which point on the line joining them will the gravitational field intensity be zero ?

Answer 1

Solution:
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.

Answer 2

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