A platform having no mass is kept on a light elastic spring . When a small particle of 0.1 kg is dropped on this spring from a height of 0.50 m , the spring is compressed by 0.02 m . From which height the particle should be dropped to produce a compression of 0.05 m ?

Explanation

To solve the problem, we will use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

### Step-by-Step Solution:

1. **Understand the Problem**: We have a particle of mass \( m = 0.1 \, \text{kg} \) dropped from a height \( h \) onto a spring. The spring compresses by \( x \) meters. We need to find the height \( h \) from which the particle should be dropped to produce a compression of \( 0.05 \, \text{m} \).

2. **Initial Conditions**:
- When the particle is dropped from a height of \( 0.50 \, \text{m} \), the spring compresses by \( 0.02 \, \text{m} \).
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