A body of mass 2 kg is dropped from rest from a height 20 m from the surface of Earth. The body hiys the ground with velocity 10 m/s, then work done `(g=10m//s^(2))`

Options

A. On the body is 100 j
B. By the gravity is 400 J
C. By the dissipative force is 300 J
D. By the disspipative force is `-300J`

Answer

To solve the problem step by step, we will calculate the work done on the body as it falls from a height of 20 m to the ground.

### Step 1: Calculate the gravitational potential energy (PE) at the height of 20 m.
The gravitational potential energy can be calculated using the formula:
\[ PE = mgh \]
Where:
- \( m = 2 \, \text{kg} \) (mass of the body)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 20 \, \text{m} \) (height)

Substituting the values:
\[ PE = 2 \, \text{kg} \times 10 \, \text{m/s}^2 \times 20 \, \text{m} \]
\[ PE = 400 \, \text{J} \]

### Step 2: Calculate the kinetic energy (KE) just before hitting the ground.
The kinetic energy can be calculated using the formula:
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( v = 10 \, \text{m/s} \) (velocity just before hitting the ground)

Substituting the values:
\[ KE = \frac{1}{2} \times 2 \, \text{kg} \times (10 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \times 2 \times 100 \]
\[ KE = 100 \, \text{J} \]

### Step 3: Calculate the work done by the gravitational force.
The work done by gravity (W) can be calculated as the change in potential energy, which is equal to the potential energy at the height minus the kinetic energy just before hitting the ground:
\[ W = PE - KE \]
Substituting the values:
\[ W = 400 \, \text{J} - 100 \, \text{J} \]
\[ W = 300 \, \text{J} \]

### Step 4: Determine the work done against dissipative forces.
The work done against dissipative forces (like air resistance) can be calculated as:
\[ W_{\text{dissipative}} = KE - W \]
Substituting the values:
\[ W_{\text{dissipative}} = 100 \, \text{J} - 300 \, \text{J} \]
\[ W_{\text{dissipative}} = -200 \, \text{J} \]

### Conclusion
The work done by gravity is \( 300 \, \text{J} \) and the work done against dissipative forces is \( -200 \, \text{J} \).