The weight of a body is directly proportional to the acceleration due to gravity ($g$). The variation of $g$ with height $h$ is given by the formula: $g_h = g \left(\frac{R}{R+h}\right)^2$ Given that the weight becomes $1/16$th of the weight on the surface, we have $g_h = \frac{g}{16}$. Substituting this into the equation: $\frac{g}{16} = g \left(\frac{R}{R+h}\right)^2$ Taking the square root on both sides: $\frac{1}{4} = \frac{R}{R+h}$ $R + h = 4R$ $h = 3R$.