A body of mass 10 kg is dropped to the ground from a height of 10 metres. The work done by the gravitational force is `(g=9.8m//sec^(2))`

Options

A. (a)`-490J`
B. (b)`+490 J`
C. (c)`-980 J`
D. (d)`+980 J`

Answer

To solve the problem of calculating the work done by the gravitational force on a body of mass 10 kg dropped from a height of 10 meters, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Mass of the body (m) = 10 kg
- Height from which the body is dropped (h) = 10 m
- Acceleration due to gravity (g) = 9.8 m/s²

2. **Calculate the Gravitational Force:**
The gravitational force (F) acting on the body can be calculated using the formula:
\[ F = m \cdot g \]
Substituting the values:
\[ F = 10 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 98 \, \text{N} \]

3. **Determine the Work Done by Gravitational Force:**
The work done (W) by the gravitational force when the body is dropped can be calculated using the formula:
\[ W = F \cdot h \cdot \cos(\theta) \]
Here, \(\theta\) is the angle between the force and the displacement. Since both the force of gravity and the displacement (downward) are in the same direction, \(\theta = 0\) degrees, and \(\cos(0) = 1\).

Thus, the equation simplifies to:
\[ W = F \cdot h \]
Substituting the values:
\[ W = 98 \, \text{N} \cdot 10 \, \text{m} = 980 \, \text{J} \]

4. **Final Result:**
The work done by the gravitational force is:
\[ W = 980 \, \text{J} \]