Question

The gravitation potential energy of a body at a distance r from the centre of the earth is U, then its weight at that point is ________.

• A. $\frac{U}{r^2}$
• B. $\frac{U}{r}$
• C. $Ur$
• D. $U{r}^3$

Answer 1

The correct option is B $\frac{U}{r}$

Gravitational potential energy $=\frac{GMm}{r}$
$\therefore \frac{GMm}{r}=U$
$\Rightarrow \frac{GMm}{r^2}=\frac{U}{r}$
$\Rightarrow mg=\frac{U}{r}$ $[\because g=\frac{GM}{r^2}]$
$\therefore$ Weight $=mg=\frac{U}{r}$