A particle of mass `1 kg` is kept on the surface of a uniform sphere of mass `20 kg` and radius `1.0 m`. Find the work to be done against the gravitational force between them to take the particle away from the sphere.

Explanation

To solve the problem of finding the work done against the gravitational force to take a particle of mass `1 kg` away from the surface of a uniform sphere of mass `20 kg` and radius `1.0 m`, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Gravitational Potential Energy Formula:**
The gravitational potential energy (U) at the surface of a uniform sphere is given by the formula:
\[ U = -\frac{GMm}{R} \]
where:
- \( G \) is the gravitational constant \( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)
- \( M \) is the mass of the sphere \( 20 \, \text{kg} \)
- \( m \) is the mass of the particle \( 1 \, \text{kg} \)
- \( R \) is the radius of the sphere \( 1.0 \, \text{m} \)

2. **Calculate the Gravitational Potential Energy at the Surface:**
Substitute the values into the formula:
\[ U = -\frac{(6.67 \times 10^{-11}) \times (20) \times (1)}{1} \]
\[ U = -1.334 \times 10^{-9} \, \text{J} \]

3. **Determine the Work Done Against Gravitational Force:**
The work done (W) to move the particle from the surface of the sphere to infinity is equal to the negative of the gravitational potential energy at the surface:
\[ W = -U = 1.334 \times 10^{-9} \, \text{J} \]

4. **Final Answer:**
The work done against the gravitational force to take the particle away from the sphere is:
\[ W = 1.334 \times 10^{-9} \, \text{J} \]