Question

A mass $2\text{kg}$ is moved from point $\text{A}$ to $\text{B}$. If the increase in kinetic energy of mass is $4\text{J}$ and work done on the mass is $-10\text{J}$, then potential difference between $\text{B}$ and $\text{A}$ ($\text{J/kg}$) is

• A. $4$
• B. $7$
• C. $-3$
• D. $-7$

Answer 1

The correct option is D $-7$

Given:

$\Delta K=4\text{J};W_{ext}=-10\text{J}$

Applying work- energy theorem,

$W_{ext}=\Delta U+\Delta K$

$\Rightarrow \Delta U=W_{ext}-\Delta K$

$\Rightarrow \Delta U=-10-4=-14\text{J}$

The change is potential is given by

$\Delta V=\Delta U/m=-14/2=-7\text{J/kg}$

Therefore, option $\left(d\right)$ is correct.

Key Concept: The change in potential is defined as the change in potential energy per unit mass.