An infinite number of particles each of mass 1kg are placed on the positive x-axis at 1m, 2m, 4m, 8m…. from the origin. The magnitude of the resultant gravitational force on 1kg mass kept at the origin is

We need to calculate the resultant gravitational force exerted by an infinite number of particles on a 1 kg mass placed at the origin.

• Mass of each particle = 1 kg
• Distance of particles from the origin: 1m, 2m, 4m, 8m, ...

The gravitational force between two masses is given by:

Where:

• G = Gravitational constant
• m₁ = m₂ = 1 kg
• r = Distance from the origin

Force exerted by the particle at distance 1m:

Force exerted by the particle at distance 2m:

Force exerted by the particle at distance 4m:

The total force is:

This is an infinite geometric series with:

• First term (a) = 1
• Common ratio (r) = 1/4

Using the sum of an infinite geometric series formula:

Final Answer:

(d) 4G / 3