the length of a simple pendulum is 84cm. what will be its time period if it was taken to moon where accelerationdue to gravity is 1/6 that on earth?
Answers
The question is slightly wrong. When we talk about a seconds pendulum, we already know that the time period is going to be 2 seconds. That is why we call it a seconds pendulum.
T=2PIE L/8
So, in this formula, T is time period, l is the effective length of a pendulum and g is the acceleration due to gravity. On the surface of the earth, the effective length of a pendulum should be 99.2 cm so that its time period becomes 2 seconds and hence, we call it a seconds pendulum. When we go the moon, the acceleration due to gravity decreases. As acceleration due to gravity is inversely proportional to the time period, the time period shall increase. But we need to keep the time period equal to 2 seconds so we will have to decrease the length of the pendulum as the time period is directly proportional to the length. So the time period decreases and returns to 2 seconds.
You can mathematically prove this by using the above formula. Take T as 2 seconds,g as 1/6 th of the acceleration due to gravity on earth and calculate the required length of the pendulum.