If a body of mass 200 g falls a height 200 m and its total P.E. is converted into K.E. at the point of contact of the body with earth surface. Then what is the decrease in P.E. of the body at the contact.
`(g=10m//s^(2))`

Options

A. 900 J
B. 600 J
C. 400 J
D. 200 J

Explanation

To solve the problem, we need to calculate the decrease in potential energy (P.E.) of a body when it falls from a height. The potential energy at a height is given by the formula:

\[ \text{P.E.} = mgh \]

where:
- \( m \) is the mass of the body,
- \( g \) is the acceleration due to gravity,
- \( h \) is the height from which the body falls.

### Step-by-Step Solution:

1. **Convert Mass from grams to kilograms**:
The mass of the body is given as 200 g. We need to convert this to kilograms since the SI unit of mass is kg.
\[ m = \frac{200 \text{ g}}{1000} = 0.2 \text{ kg} \]

2. **Identify the values**:
We have:
- \( m = 0.2 \text{ kg} \)
- \( g = 10 \text{ m/s}^2 \)
- \( h = 200 \text{ m} \)

3. **Calculate Potential Energy (P.E.)**:
Now we can substitute the values into the potential energy formula:
\[ \text{P.E.} = mgh = 0.2 \text{ kg} \times 10 \text{ m/s}^2 \times 200 \text{ m} \]

4. **Perform the multiplication**:
\[ \text{P.E.} = 0.2 \times 10 \times 200 = 0.2 \times 2000 = 400 \text{ Joules} \]

5. **Conclusion**:
The decrease in potential energy of the body at the point of contact with the earth's surface is:
\[ \text{Decrease in P.E.} = 400 \text{ Joules} \]

### Final Answer:
The decrease in potential energy of the body at the contact is **400 Joules**.

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