An infinite number of particles each of mass `m` are placed on the positive X-axis of `1m, 2m, 4m, 8m,...` from the origin. Find the magnitude of the resultant gravitational force on mass `m` kept at the origin.

Explanation

To find the magnitude of the resultant gravitational force on a mass \( m \) placed at the origin due to an infinite number of particles located at distances \( 1m, 2m, 4m, 8m, \ldots \) along the positive X-axis, we can follow these steps:

### Step 1: Identify the gravitational force due to a single mass
The gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by the formula:
\[ F = \frac{G m_1 m_2}{r^2} \]
In our case, the mass at the origin is \( m \) and the masses located at distances \( 1m, 2m, 4m, 8m, \ldots \) are also \( m \).
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