Couple of days before I came across a question something like this
A particle is moving in a conservative force field from point $A$ to point $B$. Let $U_A$ and $U_B$ be the potential energies of particle at points $A$ and $B$ respectively and $W_C$ is the work done in the process in moving the particle from $A$ to $B$. (Take work done to be positive)
And we needed to find the correct relations among some alternatives. What I figured out is as follows:
- Potential Energy of particle is equal to $negative$ of $work$ $done$ by $conservative$ force.
And Work done is equal to Change in Potential energy of particle.
So I found the alternatives as $W_C$=$-(U_B-U_A)$ i.e $W_C$=$(U_A-U_B)$ as correct , but correct answer is $W_C$=$(U_B-U_A)$. I think there is some trick in the last statement of question that "(Take work done to be positive) " But if I take work done to be positive then $U_B$<$U_A$ but this also contradicts the answer as the answer is $U_B$>$U_A$
This made a huge confusion in my mind. Please tell me if I am missing some concept. And do tell me the correct answers too.