On the surface of earth, the time period of a simple pendulum is T_(e). When the pendulum is taken to a height of 2R above the surface of earth, the time period becomes T_(h). (R is radius of earth.) The value of (T_(e))/(T_(h)) is

On the surface of earth, the time period of a simple pendulum is T_(e)

1.	On the surface of earth, the time period of a simple pendulum is T_(e). When the pendulum is taken to a height of 2R above the surface of earth, the time period becomes T_(h). (R is radius of earth.) The value of (T_(e))/(T_(h)) is
Answer» `1 : 9` `9 : 1` `1 : 3` `3 : 1` Solution :As time PERIOD of a SIMPLE PENDULUM `T = 2pisqrt((l)/(g))` On earth.s surface `g_(e) = (GM)/(R^(2))` At a height `h = 2R, g_(h) = (GM)/((R + 2R)^(2)) = (GM)/(9R^(2))` `(T_(e))/(T_(h)) = sqrt((g_(h))/(g_(e))) = sqrt((GM.R^(2))/(9R^(2).GM))` `(T_(e))/(T_(h)) = sqrt((1)/(9)) = 1:3`