Question

The gravitational potential energy of a body of mass$m$at a distance $r$ from the center of the earth is$U$. What is the weight of the body at this distance?

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

Answer 1

The correct option is C

$\frac{U}{r}$

Step 1: Given data

The mass of the body$=m$

The distance from the center of the earth$=r$

Gravitational potential energy$=U$

Step 2: Formula Used

We know that the gravitational potential energy, $U=\frac{GMm}{r}$

And also, $g=\frac{GM}{r^2}$, where $g$is the gravity of earth.

Step 3: Calculating weight

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

Divide from $\frac{1}{r}$both sides,

Therefore,

$\frac{U}{r}=\frac{GMm}{r^2}$

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

Then,

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

As we know the weight of a body is equal to $W=mg$

Therefore, the weight $mg=\frac{U}{r}$.

Hence, option C is correct.