Final answer:
The time period of a simple pendulum that crosses its mean position 50 times in 10 seconds is 0.4 seconds. It is calculated by dividing the total time by the number of full cycles (25 in this case).
Step-by-step explanation:
Calculating Time Period of a Simple Pendulum
When a bob of a simple pendulum crosses its mean position 50 times in 10 seconds, it means it has completed 25 full swings (cycles), as each cycle includes crossing the mean position twice. To calculate the time period of the pendulum's oscillation, we divided the total time taken by the number of full cycles:
Time taken for one oscillation (period) = Total time ÷ Number of cycles
Time period (T) = 10 s ÷ 25 cycles = 0.4 s
The time period of the pendulum is 0.4 seconds