Question

An object of mass $2\text{kg}$ is moved from infinity to a point $\text{P}$. Initially the object was at rest but on reaching $\text{P}$ its speed becomes $2\text{m/s}$. If the work done in moving that object is $-4\text{J}$, then find the ratio of potential energy to mass at point $\text{P}$ (in $\text{J/kg}$) is

• A. $8$
• B. $-8$
• C. $4$
• D. $-4$

Answer 1

The correct option is D $-4$

As we know that potential energy at infinity for any object remains zero.

$\therefore U_{\infty }=0$

From question,

$K{E}_{\infty }=0$ because object was at rest.

Applying work-energy theorem,

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

$\Rightarrow -4=U_f-U_i+K{E}_f-K{E}_i$

$\Rightarrow -4=U_f-0+\frac{1}{2}m{v}^2-0$

Given: $m=2\text{kg};v=2\text{m/s}$

$\Rightarrow U_f=-4-\frac{1}{2}\times 2\times (2{)}^2=-8\text{J}$

$\therefore$ potential energy per unit mass $=\frac{U_f}{m}=\frac{-8}{2}=-4\text{J/kg}$

Hence, option $\left(d\right)$ is the correct answer.