Question

The potential energy of a system increases if work is done

• A. upon the system by a non conservative force.
• B. on the system against a conservative force.
• C. by the system against a non conservative force.
• D. upon the system by a conservative force.

Answer 1

The correct option is B on the system against a conservative force.

Potential energy $U$ for a system is defined as:
$W_{\text{int}}=-\Delta U=-(U_f-U_i)...\left(1\right)$
${\int }_i^f\overrightarrow{F}\cdot \overrightarrow{dr}=-(U_f-U_i)...\left(2\right)$
$\Rightarrow$Where $\overrightarrow{F}$ is an internal conservative force, and $W_{\text{int}}$ is work done by the internal conservative force.
$\Rightarrow$ If $U$ increases then $U_f>U_i$ , or the term $-(U_f-U_i)$ will be $-ve$.

$\Rightarrow$ $W_{\text{int}}$ will become $-ve$
$\therefore$ System has done work against the conservative force