Question

Two spherical balls of mass 1 kg and 4 kg are separated by a distance of 12 cm. The distance from 1 kg at which the gravitational force on any mass becomes zero.

• A. $4cm$
• B. $12cm$
• C. $6cm$
• D. $8cm$

Answer 1

The correct option is A $4cm$

We know,

The gravitational force, $F=\frac{G{m}_1{m}_2}{r^2}$

Given,

$m_1=1kg$

$m_2=4kg$

$d=12cm$

Let the distance at which the force due to gravity is $0$ is $x$. This means that force due to both the object at this point are equal and opposite.

Distance of this point $=xcm$ from $1kg$ ball

$⟹$ Distance of this point from $4kg$ ball $=d-x=12-x$

So,

$\frac{Gm{m}_1}{x^2}=\frac{Gm{m}_2}{(12-x{)}^2}$

$⟹\frac{1}{x^2}=\frac{4}{(12-x{)}^2}$

$⟹\frac{1}{x}=\frac{2}{12-x}$

$⟹2x=12-x$

$⟹3x=12$

$⟹x=4cm$

Hence at $4cm$ from $1kg$ ball the net force is zero.