Two heavy sphere each of mass `100 kg` and radius `0.10 m` are placed `1.0 m` apart on a horizontal table. What is the gravitational field and potential at the mid point of the line joining the centres of the sphere? Is an object placed at that point in equilibrium? If so, is the equilbrium stable or unstable.

Explanation

To solve the problem step by step, we will calculate the gravitational field and potential at the midpoint between the two spheres and analyze the equilibrium condition.

### Step 1: Understand the Setup
We have two spheres, each with a mass \( m = 100 \, \text{kg} \) and radius \( r = 0.10 \, \text{m} \), placed \( d = 1.0 \, \text{m} \) apart on a horizontal table. The midpoint between the two spheres is at a distance of \( 0.5 \, \text{m} \) from each sphere.

### Step 2: Calculate the Gravitational Field at the Midpoint
The gravitational field \( E \) due to a mass \( m \) at a distance \( r \) is given by the formula:
\[
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