What is the periodof a pendulum that makes 50 cycles in 9 seconds
Answers
A “seconds pendulum” is about 1 meter long. This was in fact considered for the definition of a meter, as the construction of pendulums was well-known at the time, a second was well-defined, and a seconds pendulum was in the right range for the unit they wanted. Unfortunately for that definition, the critical value for g , the gravitational acceleration, varies significantly from place to place, so the length of the seconds pendulum changes from place to place.
However, a seconds pendulum doesn’t have a period of 1 second, it has a period of 2 seconds. It takes 1 second to swing in one direction, and another second to swing back. Since clocks typically ‘tick’ once per swing, or twice per period, a seconds pendulum clock ticks once per second.
The period of a pendulum is proportional to the square root of its length, or turned around, the length of a pendulum is proportional to the square of its period. As such, halving the period of a pendulum will quarter (half squared) its length. Since a seconds pendulum, with a period of 2 seconds, has a length of 1 meter, a pendulum with a period of 1 second will have a length of 14 meters, or about 25 cm.
The actual formula is T=2πLg−−√ or L=T2g4π2 . Since we are dealing with T=1s , this becomes L=g4π2s2 , and is directly proportional to g .
At the equator, the combined effects of the equatorial bulge and centrifugal force from the rotating Earth reduce g to g=9.78m/s2 , so we have L=9.78m4π2≈24.77cm , although the precision of the result is probably a bit more than we can get out of the measurement of g .
At the poles, the value of g becomes g=9.832m/s2 , so we have L=9.832m4π2≈24.90cm . Again, this is probably more precise than is justified.
This makes it reasonable to say that the initial estimate of “about 25 cm” is close enough, within the precision we need.
Practically, this is solved in horology by making the pendulum length effectively adjustable. The bob may have a threaded extension on the bottom with a nut on it. If the pendulum is running fast, the nut is turned so that the center of mass of the pendulum is lower. If the pendulum is running slow, the nut is raised. Other clocks provide a way to add weights to the top of the bob, and by adjusting the amount of added weight, it adjusts the center of mass of the bob to adjust the timing slightly. The pendulum driving the clock in Elizabeth Tower in London (home of the bell Big Ben) has a stack of pennies on top of the bob, which are occasionally adjusted.
.
.
.
Hope it helps u
Mark me as brainliest