Mathematics
Grade10
Easy

Question

Big Ben’s pendulum takes 4 s to swing back and forth. The formula straight t space equals space 2 straight pi space square root of straight L over 32 end root  gives the swing time, t, in seconds, based on the length of the pendulum, L, in feet. What is the minimum length necessary to build a clock with a pendulum that takes longer than Big Ben’s pendulum to swing back and forth?

  1. 32 feet
  2. 41 feet
  3. 40 feet
  4. 56 feet

Hint:

In this question, we have to find the minimum length necessary to build a clock with a pendulum that takes longer than Big Ben’s pendulum to swing back and forth, if Big Ben’s pendulum takes 4 s to swing back and forth and the formula straight t space equals space 2 straight pi space square root of straight L over 32 end root gives the swing time, t, in seconds, based on the length of the pendulum, L, in feet.

The correct answer is: 41 feet


    straight t space equals space 2 straight pi space square root of straight L over 32 end root
2 straight pi space square root of straight L over 32 end root space greater than space 4 space not stretchy rightwards double arrow space open parentheses square root of straight L over 32 end root close parentheses squared space open parentheses fraction numerator 4 over denominator 2 straight pi 1 end fraction close parentheses squared
not stretchy rightwards double arrow space straight L over 32 space greater than space 4 over straight pi space not stretchy rightwards double arrow space straight L space greater than space 128 over straight pi

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