The length of a seconds pendulum is 1.06m. Find the length of a pendulum whose time period is 1.2 seconds.
Answers
Answer:
The first part of the question is a statement. The second part of the question may not be related to the first part as the calculated length of the pendulum may come out different from the calculation as shown below. Let’s see : The equation that connects the time period of oscillation to the vertical length of the pendulum and the acceleration due to gravity (g) is as follows : T = 2p•(L/g)^1/2, where T is the time period of each swing at a small angle of swing, p is pi which is a constant, L is the vertical length of the pendulum, and g is the acceleration due to gravity. So we are given T in the above question, and we need to find L. There are only two variables in the equation with g being nearly the same all over the earth (9.81m/s^2), and these are T and L which are inherently related to each other through the above equation. So let’s solve the equation for L: L = T^2•g/4p^2, which will give us 0.358 meter. As you can see the answer is 0.36 m rounding off to 2 decimal places for the second part of the question, and has nothing to do with the first part of the question ! We certainly can calculate what would have been the T for a pendulum of length 1.06 m. That would give us a T of 2.07 seconds. The equation for the pendulum’s time period of oscillation (or swing) shows also that T is directly proportional to the square root of the length of the pendulum, which is the same thing mathematically as saying that T^2 is directly proportional to the length L of the pendulum, and inversely proportional to the acceleration due to gravitation. Longer the L greater will be T or T^2, and conversely shorter the L, smaller will be T^2 or T generally speaking. If we are on another planet with a different g value, then the inverse relationship will hold still. Greater the g value, faster the pendulum will swing therefore shorter will be the T value, and lower the g, longer will be the T, or time period of oscillation or swing generally speaking. The pendulum experiment to determine the value of g is a great physics experiment for the high school physics class room, and college classroom. There you can vary the length of the pendulum and calculate the T for each length and plot a graph of L against T ^2, with say L on the y axis, and T ^2 on the x axis which can be used to calculate the slope or rate of rise of the graph. It will be a linear graph. Once you calculate the slope, it can be equated to the mathematical expression for the slope in the equation which is g/4p^2, and g can be calculated with the experimental data. Let’s say the slope is S then S = g/4p^2 which will give you g = 4Sp^2. It is all beautiful basic physics that relates gravitation to motion of a pendulum. So you can calculate the g value anywhere on earth, on the moon, and on any other planet or moon where you can land and conduct this simple and beautiful experiment… Kaiser T, MD (Life long physics, math, cosmology, and science proponent).
Answer:
0.38m
its correct ans ur ans..is wrong