Pendulums

Step 1: Formula for Time Period of a Simple Pendulum The time period of a simple pendulum is given by the formula: Where: - is the length of the string, - is the acceleration due to gravity at the surface of the Earth. Step 2: Adjusting for the Height of the Pendulum The pendulum is at a height equal to the Earth's radius, meaning the effective value of will change. The acceleration due to gravity at a height above the Earth's surface (where ) is given by the formula: Since , the expression simplifies to: Thus, the effective value of gravity at this height is . Step 3: Calculating the Time Period Now, substitute the effective gravity into the formula for the time period: Given that and , we get: Thus, the time period is: Step 4: Conclusion The time period of oscillation is approximately 8 seconds. Thus, the correct answer is:

Concept: Gravity variation with height: Step 1: {\color{red}Given height.} Step 2: {\color{red}Time period.} Step 3: {\color{red}Substitute .}