24 Questions
What is the primary aim of the experiment described?
To measure the value of 'g' using Kater's pendulum
What is the purpose of the two movable knife edges K1 and K2 in Kater's pendulum?
To adjust the centre of gravity of the pendulum
What is the significance of the centre of gravity lying near one of the knife edges?
To make the time periods of the pendulum about the two knife edges equal
What is the material of the cylinder W2?
Wood
What is the length of the meter rod used in the experiment?
100cm
What is the principle behind Kater's pendulum?
The centre of suspension and centre of oscillation are interchangeable
What is the purpose of placing a heavy mass at one end of a Kater's pendulum?
To ensure the pendulum oscillates smoothly
What is the standard value of acceleration due to gravity in m/s2?
9.8
What is the typical unit of distance between the two knife edges in a Kater's pendulum?
Meter
What is the purpose of measuring the time periods of oscillations in a Kater's pendulum?
To determine the acceleration due to gravity
What is the significance of the Kater's pendulum experiment?
It measures the acceleration due to gravity with high accuracy
What is the name of the reference book published by Oscar publications in 2009?
Physics Experiments for Engineers
What is the purpose of Bessel's approximation in the determination of acceleration due to gravity?
To avoid the difficulty of setting the Kater's pendulum for equal time periods
What is the condition for equation (2) to be applicable?
When T1 and T2 are very close to each other (difference less than 1 percent)
What is the symbol 'Ɩ1' and 'Ɩ2' representing in the given formula?
Distances between knife-edges and CG of the pendulum
What is the formula used to determine the acceleration due to gravity 'g'?
g = 8𝜋2 𝑇12+𝑇22 / 𝑙1+𝑙2 + 𝑙1−𝑙2
What is the significance of the distance between the knife edges in Kater's pendulum?
It is equal to the length of the equivalent simple pendulum
What is the purpose of the Kater's pendulum?
To calculate the acceleration due to gravity
What is the main purpose of ensuring the amplitude of vibration is small?
To ensure the motion of the pendulum satisfies the condition of simple harmonic motion
Why is a glass surface on a rigid support used in the experiment?
To avoid friction
What is the purpose of moving the mass M up or down during the experiment?
To make the time periods nearly equal
What is the formula used to calculate the value of g in the experiment?
Not mentioned in the experiment
Why is the experiment repeated by changing the distance between the two knife edges?
To increase the accuracy of the measurement of g
What is the purpose of noting the time period after the pendulum has made a few oscillations?
To allow the pendulum to settle into a steady state of motion
Study Notes
Kater's Pendulum Experiment
- Kater's pendulum is a compound pendulum used to measure the value of acceleration due to gravity (g).
- It consists of a long metallic rod with a heavy metallic cylinder at one end and an identical wooden cylinder at the other end, with a smaller metallic cylinder at the middle.
Principle and Theory
- The principle of Kater's pendulum is based on the idea that the center of suspension and center of oscillation are interchangeable.
- The pendulum is adjusted so that the time periods of oscillation about two knife edges (K1 and K2) are exactly equal.
- The distance between the knife edges is equal to the length of an equivalent simple pendulum, whose time period is given by T=2π√𝑙/𝑔.
Formula Used
- The formula used to determine acceleration due to gravity (g) is: g= 8𝜋2 𝑇12+𝑇22 𝑇12−𝑇22 𝑙1+𝑙2 + 𝑙1−𝑙2
Bessel's Approximation
- Bessel's approximation is used when the two time periods are not exactly equal, making it easier to set up the experiment.
- The formula becomes: g= 8𝜋 𝑇12+𝑇22 𝑙1+𝑙2 when T1 and T2 are very close to each other (difference less than 1 percent).
Precautions and Procedure
- Precautions include ensuring parallel knife-edges, small amplitude of vibration, and avoiding friction by using a glass surface on a rigid support.
- The procedure involves suspending the pendulum from the knife edges, finding the time periods, and measuring the distance between the knife edges.
Calculations and Results
- The value of g is calculated using the formula, and the experiment can be repeated by changing the distance between the knife edges.
Explore the concept of measuring the acceleration due to gravity (g) using Kater's pendulum in this experiment. Learn about the equipment and procedures involved in the experiment. This quiz is based on the University Institute of Engineering's Department of Academic Unit-1 to 5 course.
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