If you stand on a tall ladder so that your distance from the Earth's centre becomes $2R$, your weight becomes what fraction of its value on the surface?

1. Weight $W = mg = \dfrac{GMm}{r^2}$, so $W \propto \dfrac{1}{r^2}$ for fixed mass. 2. At the surface $r = R$; on the ladder $r = 2R$. 3. The ratio $\dfrac{W_{2R}}{W_R} = \dfrac{R^2}{(2R)^2} = \dfrac{1}{4}$. 4. So weight falls to one-fourth; 'one-half' wrongly assumes $W \propto 1/r$ and is the trap. _Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.19_