Question

A person brings a mass of $2\text{kg}$ from $\text{A}$ to $\text{B}$. The increase in kinetic energy of mass is $4\text{J}$ and work done by the person on the mass is $-10\text{J}$. The potential difference between $\text{B}$ and $\text{A}$ is $($in $\text{J/kg})$

• A. $4$
• B. $7$
• C. $-3$
• D. $-7$

Answer 1

The correct option is D $-7$

By work energy theorem, external workdone on the system is equal to the sum of change in potential and kinetic energy of system,
$$W_{ext}=\Delta U+\Delta K$$Given,
Mass, $m=2\text{kg}$

External work done by the person, $W_{ext}=-10\text{J}$

Change in kinetic energy, $\Delta K=4\text{J}$.

Substituting the values in the above equation, we get
$-10=\Delta U+4$

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

The change in potential is given by
$$\Delta V=\frac{\Delta U}{m}$$ $\Rightarrow \Delta V=\frac{-14}{2}$

$\therefore \Delta V=-7\text{J/kg}$

Hence, option (c) is the correct answer.

Key Concept: The change in potential is defined as the change in potential energy per unit mass. Why this question: To familiarize students with the relationship between potential energy and potential.