An interesting analogy based upon energy density. Find the work done by external agent to filll the mass m in a sherical volume of Radius R. (You may takethe example of earth)

Explanation

To find the work done by an external agent to fill a mass \( m \) in a spherical volume of radius \( R \), we can follow these steps:

### Step 1: Understand the Concept of Gravitational Potential Energy
The gravitational potential energy \( U \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by the formula:
\[ U = -\frac{G m_1 m_2}{r} \]
where \( G \) is the gravitational constant.
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