The height at which the acceleration due to gravity becomes g 16 (where, g= acceleration due to gravity on the surface of the earth) in terms of R is, if R is the radius of earth.

Step-by-step solution

The acceleration due to gravity at a height h above the surface of the earth is given by the formula g_h = g ( R R + h )^2 , where g is the acceleration due to gravity at the surface and R is the radius of the earth. Given that g_h = g 16 , we substitute this into the equation: g 16 = g ( R R + h )^2 Dividing both sides by g and taking the square root of both sides: 1 4 = R R + h Cross-multiplying gives: R + h = 4R h = 3R Answer: 3 R