Question

The gravitational potential energy of a body at a distance 'r' from the centre of the earth is 'U'. Its weight at a distance 'R' from the centre of the earth is

• A. $\frac{Ur}{R}$
• B. $\frac{Ur}{R^2}$
• C. $\frac{U{r}^2}{R^2}$
• D. None of these

Answer 1

The correct option is A $\frac{Ur}{R}$

Gravitational potential energy ,$U=\frac{GMm}{r}.$

For calculating the weight at distance $2r$ from centre of earth , we need to get $m\times g.$

But here acceleration due to gravity , $g$ is not equal to $9.8m/s^{-2}.$

Calculation of g can be done using the formula :-

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

Therefore, the value of g at a distance of $R=\frac{GM}{R^2}$

Thus , weight of the body at a distance $R$ from the body $=mg=\frac{GMm}{R}=\frac{Ur}{R}$

Henece option A is correct