Question

The gravitational potential difference between the surface of a planet and a point $20\, m$ above the surface, is $ 2$ joule $/ kg$. If the gravitational field is uniform, then the work done in carrying a $5 kg$ body to a height of $4 m$ above the surface is

• A. $2 J $
• B. $20 J$
• C. $40 J$
• D. $10 J$

Answer 1

Answer: (A)

$\Delta U=mg \,\Delta h$
$\Delta V=\frac{\Delta U}{m}=g \Delta h$
$ \Rightarrow \frac{2 J }{ kg }=g(20 m )$
and $\Delta V'=g(4 m ) ; \frac{\Delta V'}{2}=\frac{4}{20}$
$\Delta V=\frac{4 \times 2}{20}=0.4 \frac{ J }{ kg }$
$W_{ ex }=m \Delta V'=(5 kg ) \times 0.4 \frac{ J }{ kg }=2 J$