Question

An object of mass $5\text{kg}$ is moved from infinity to a point $\text{A}$. Initially the object was at rest but on reaching $\text{A}$ , its speed becomes $5\text{m/s}$. If the work done in moving that object is $-25\text{J}$, then find the ratio of potential energy to mass at point $\text{A}$ (in $\text{J/kg}$) is

• A. $-35\text{J/kg}$
• B. $-87.5\text{J/kg}$
• C. $-17.5\text{J/kg}$
• D. $-7\text{J/kg}$

Answer 1

The correct option is C $-17.5\text{J/kg}$

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,

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

$\Rightarrow -25=U_A-U_{\infty }+K{E}_A-K{E}_{\infty }$

$\Rightarrow -25=U_A-0+\frac{1}{2}m{v}^2-0$

Given: $m=5\text{kg};v=5\text{m/s}$

$\Rightarrow U_A=-25-\frac{1}{2}\times 5\times (5{)}^2=-87.5\text{J}$

$\therefore$ potential energy per unit mass

$=\frac{U_A}{m}=\frac{-87.5}{5}=-17.5\text{J/kg}$

Hence, option (c) is the correct answer.