The length of a seconds pendulum at a height h = 2 R from earth surface will be: (Given: R = Radius of earth and acceleration due to gravity at the surface of earth g = π 2 m s - 2 )

Step-by-step solution

The acceleration due to gravity at height 2 R from the surface of the Earth will be, g ' = g R 2 R + h 2 ⇒ g ' = g R 2 R + 2 R 2 ⇒ g ' = g 9 Length of the second's pendulum at the surface of the Earth is 1   m . Since, time period of a pendulum is given by, T = 2 π l g ⇒ T ' T = l ' l × g g ' ⇒ 1 = l ' l × g g ' ⇒ l ' = l 9 = 1 9   m