A body of mass 2 kg is dropped from rest from a height 20 m from the surface of Earth. The body hits 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 potential energy at the height, the kinetic energy just before hitting the ground, and then determine the work done by gravitational and dissipative forces.

### Step 1: Calculate Potential Energy at Height
The potential energy (PE) of the body at the height can be calculated using the formula:
\[ \text{PE} = mgh \]
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:
\[ \text{PE} = 2 \, \text{kg} \times 10 \, \text{m/s}^2 \times 20 \, \text{m} = 400 \, \text{J} \]

### Step 2: Calculate Kinetic Energy Just Before Hitting the Ground
The kinetic energy (KE) of the body just before it hits the ground can be calculated using the formula:
\[ \text{KE} = \frac{1}{2} mv^2 \]
Where:
- \( v = 10 \, \text{m/s} \) (velocity just before hitting the ground)

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

### Step 3: Calculate Work Done by Gravity
The work done by gravity (W_gravity) is equal to the potential energy of the body when it was at the height:
\[ W_{\text{gravity}} = \text{PE} = 400 \, \text{J} \]

### Step 4: Calculate Net Work Done on the Body
According to the work-energy theorem, the net work done on the body is equal to the change in kinetic energy:
\[ W_{\text{net}} = \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \]
Where:
- \( KE_{\text{initial}} = 0 \, \text{J} \) (since it was dropped from rest)
- \( KE_{\text{final}} = 100 \, \text{J} \)

Thus:
\[ W_{\text{net}} = 100 \, \text{J} - 0 \, \text{J} = 100 \, \text{J} \]

### Step 5: Calculate Work Done by Dissipative Forces
The work done by dissipative forces can be calculated using the relationship:
\[ W_{\text{net}} = W_{\text{gravity}} + W_{\text{dissipative}} \]
Rearranging gives:
\[ W_{\text{dissipative}} = W_{\text{net}} - W_{\text{gravity}} \]
Substituting the values:
\[ W_{\text{dissipative}} = 100 \, \text{J} - 400 \, \text{J} = -300 \, \text{J} \]

### Summary of Results
- Work done by gravity: \( 400 \, \text{J} \)
- Net work done on the body: \( 100 \, \text{J} \)
- Work done by dissipative forces: \( -300 \, \text{J} \)