Question

The gravitational potential energy of a body at a distance $r$ from the centre of earth is $U$. Its weight at a distance $2r$ from the centre of earth is

• A. $\frac{U}{r}$
• B. $\frac{U}{2r}$
• C. $\frac{U}{4r}$
• D. $\frac{U}{\sqrt{2}r}$

Answer 1

Answer: (C)

$\frac{U}{4r}$

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

$\therefore -GM=\frac{Ur}{m}$

$E=-\frac{GM}{(2r{)}^2}=\frac{\left(\frac{Ur}{m}\right)}{4r^2}=\frac{U}{4mr}$

$F=mE=\frac{U}{4r}$