Question

Two massive objects of masses 5 kg and 20 kg are separated by a distance of 25 m, then the distance at which no net gravitational force is felt due to these masses, is

• A. 8.33 m from 5 kg object
• B. 25 m from 20 kg object
• C. 50 m from 20 kg object
• D. 5 m from 5 kg object

Answer 1

The correct option is A. 8.33 m from 5 kg object

The gravitational force is purely attractive in nature. Therefore the point of zero gravitational field will be present somewhere in between the two masses.

The distance at which no net gravitational force acts, means the force due to both masses balance each other.

Let the distance be x from 5kg object. Thus, the distance from 20 kg object is 25-x.

Now we have,

$F_5=F_{20}$

$\frac{\left(G\right)\left(5\right)\left(m_0\right)}{x^2}=\frac{\left(G\right)\left(20\right)\left(m_0\right)}{(25-x{)}^2}$

$(25-x{)}^2=4x^2$

$25-x=2x$

On solving we get,

x = 8.33 m

8.33 m from 5 kg object.