Question

The gravitational potential difference between the surface of a planet and a point $20$m above it is $16$ J/kg. Calculate the work done in moving a $4$kg body by $8$m on a slope of ${60}^o$ from the horizontal.

Answer 1

Here, $h=20$m.
Gravitational potential difference $=16$J $k{g}^{-1}$.
The vertical distance through which the body has to be raised is $8\sin {60}^o=8\times (\sqrt{3}\times )=4\sqrt{3}$m.
Since gravitational potential difference for a distance of $20$m is $16$ J/kg, hence the potential difference for a distance of $4\sqrt{3}$m for a body of mass $4$kg is $(\frac{16}{20}\times 4\sqrt{3})$J $k{g}^{-1}$.
Work done in lifting a $4$kg body through a vertical height of $4\sqrt{3}$m is
$(\frac{16}{20}\times 4\sqrt{3})\times 4=\frac{64\times 1.732}{5}=22.16$J