The time taken by simple pendulum for one oscillation is T on earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. The value of x is

Step-by-step solution

The time period of a simple pendulum on the surface of the earth is given by T = 2 L g . The acceleration due to gravity at a height h above the earth's surface is g' = g (1 + h R )^2 . Given h = R , we have g' = g (1 + R R )^2 = g 4 . The new time period T' at height R is T' = 2 L g' = 2 L g 4 = 2 2 L g = 2T . Since T' = xT , we get x = 2 . Answer: 2