Potential energy of a body in position A is-40J. Work done by conservative force in moving the body from A to B is`-20J`. Find potential energy of the body in position B.

Explanation

To find the potential energy of the body in position B, we can use the relationship between work done by conservative forces and potential energy. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Potential energy at position A (UA) = -40 J
- Work done by conservative force in moving from A to B (W_AB) = -20 J

### Step 2: Use the work-energy principle
For conservative forces, the work done (W_AB) is equal to the change in potential energy between two positions:
\[ W_{AB} = U_A - U_B \]

### Step 3: Substitute the known values into the equation
We can rearrange the equation to find the potential energy at position B (UB):
\[ W_{AB} = U_A - U_B \]
Substituting the known values:
\[ -20 J = -40 J - U_B \]

### Step 4: Solve for UB
Now, we can isolate UB:
\[ -20 J = -40 J - U_B \]
Adding 40 J to both sides:
\[ -20 J + 40 J = -U_B \]
\[ 20 J = -U_B \]
Now, multiply both sides by -1:
\[ U_B = -20 J \]

### Step 5: Conclusion
The potential energy of the body in position B is:
\[ U_B = -20 J \]

### Summary
Thus, the potential energy of the body at position B is -20 Joules.

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