In deep space, sphere A of mass 20 kg is located at the origin of an x axis and sphere B of mass 10 kg is located on the axis at x = 0.95 m. Sphere B is released from rest while sphere A is held at the origin. (a) What is the gravitational potential energy of the two-sphere system just as B is released? (b) What is the kinetic energy of B when it has moved 0.15 m toward A?

Explanation

To solve the problem step by step, we will break it down into two parts as per the question.

### Part (a): Gravitational Potential Energy of the Two-Sphere System Just as B is Released

1. **Identify the masses and their positions**:
- Mass of sphere A, \( m_A = 20 \, \text{kg} \) (at the origin, \( x = 0 \, \text{m} \))
- Mass of sphere B, \( m_B = 10 \, \text{kg} \) (at \( x = 0.95 \, \text{m} \))

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