At two positons kinetic energy and potential energy of a particle are `K_(1) =10J: U_(1) =-20J, K_(2) = 20 J, U_(2)=-10 J`. In moving from 1 to 2 .

Options

A. work done by conservative forces is positive.
B. work done by conservative forces is negative.
C. work done by all the forces is positive .
D. work done by all the forces is negative.

Explanation

To solve the problem, we need to analyze the kinetic and potential energies at two positions and determine the work done by conservative forces and by all forces as the particle moves from position 1 to position 2.

### Step 1: Identify the given values
We have the following values:
- Kinetic energy at position 1, \( K_1 = 10 \, \text{J} \)
- Potential energy at position 1, \( U_1 = -20 \, \text{J} \)
- Kinetic energy at position 2, \( K_2 = 20 \, \text{J} \)
- Potential energy at position 2, \( U_2 = -10 \, \text{J} \)

### Step 2: Calculate the work done by conservative forces
The work done by conservative forces can be calculated using the change in potential energy:
\[ W_{\text{conservative}} = U_1 - U_2 \]
Substituting the values:
\[ W_{\text{conservative}} = (-20) - (-10) = -20 + 10 = -10 \, \text{J} \]
This indicates that the work done by conservative forces is negative.

### Step 3: Calculate the work done by all forces
The work done by all forces can be calculated using the change in kinetic energy:
\[ W_{\text{all}} = K_2 - K_1 \]
Substituting the values:
\[ W_{\text{all}} = 20 - 10 = 10 \, \text{J} \]
This indicates that the work done by all forces is positive.

### Step 4: Summarize the results
From the calculations:
- Work done by conservative forces: \( W_{\text{conservative}} = -10 \, \text{J} \) (negative)
- Work done by all forces: \( W_{\text{all}} = 10 \, \text{J} \) (positive)

### Conclusion
Based on the results:
- The work done by conservative forces is negative.
- The work done by all forces is positive.

Thus, the correct options are:
- Work done by conservative forces is negative.
- Work done by all forces is positive.