In position A kinetic energy of a particle is 60 J and potential energy is -20 J. In position B, kinetic energy is 100 J and potential energy is 40 J. Then, in moving the particle from A to B

Options

A. work done by conservative forces is 50 J
B. work done by external forces is 40 J
C. net work done by all the forces 40 J
D. net work done by all the forces 100 J

Explanation

To solve the problem step by step, we will analyze the given information about the kinetic and potential energies at positions A and B, and then calculate the work done by conservative and external forces.

### Step 1: Identify the given values
- At position A:
- Kinetic Energy (KE_A) = 60 J
- Potential Energy (PE_A) = -20 J

- At position B:
- Kinetic Energy (KE_B) = 100 J
- Potential Energy (PE_B) = 40 J

### Step 2: Calculate the work done by the conservative force
The work done by the conservative force can be calculated using the formula:
\[ W_{\text{conservative}} = PE_A - PE_B \]
Substituting the values:
\[ W_{\text{conservative}} = (-20 \, \text{J}) - (40 \, \text{J}) \]
\[ W_{\text{conservative}} = -20 - 40 = -60 \, \text{J} \]

### Step 3: Calculate the work done by the external force
The work done by the external force is given by the change in total mechanical energy (sum of kinetic and potential energies):
\[ W_{\text{external}} = (KE_B + PE_B) - (KE_A + PE_A) \]
Substituting the values:
\[ W_{\text{external}} = (100 \, \text{J} + 40 \, \text{J}) - (60 \, \text{J} - 20 \, \text{J}) \]
\[ W_{\text{external}} = 140 \, \text{J} - 40 \, \text{J} \]
\[ W_{\text{external}} = 100 \, \text{J} \]

### Step 4: Calculate the net work done by all forces
The net work done by all forces is the sum of the work done by the external force and the work done by the conservative force:
\[ W_{\text{net}} = W_{\text{external}} + W_{\text{conservative}} \]
Substituting the values:
\[ W_{\text{net}} = 100 \, \text{J} + (-60 \, \text{J}) \]
\[ W_{\text{net}} = 100 - 60 = 40 \, \text{J} \]

### Conclusion
The net work done by all forces in moving the particle from position A to position B is **40 J**.

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