Question

If the gravitational 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. $Ur$
• B. $\frac{U}{2r}$
  
• C. $\frac{U}{4r}$
• D. $\frac{U}{r}$

Answer 1

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

The magnitude of gravitational potential energy at a distance $r$ from the center of the earth is given by

$U=\frac{GMm}{r}$

Where $M$ is the mass of the earth and $m$ the mass of the body.

And we know that acceleration due to gravity at a distance $r$ from the center of the earth,

$g=\frac{GM}{r^2}$

So, weight of the body will be

$W=mg=m\frac{GM}{r^2}$

$\Rightarrow W=\frac{GMm}{r}\times \frac{1}{r}=\frac{U}{r}$

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