T is the time period of simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be:

Step-by-step solution

Time period of a simple pendulum at Earth's surface is given by T = 2 π l g . When distance from centre of Earth, i.e., at h = R , acceleration due to gravity is g ' = g 1 + h R 2 = g 2 2 = g 4 Now, time period is   x T = 2 π l g 4 ⇒ x T = 2 × 2 π l g ⇒ x T = 2 T ⇒ x = 2 Thus, x = 2 .