Before beginning, I recommend that you understand Pendulum by clicking here and understand Moment of Inertia by clicking here, since questions are asked from them.
Which is better between Kater’s Pendulum and Bar Pendulum? Why?
Kater’s pendulum is generally considered superior to a bar pendulum for accurate gravity measurements because it eliminates the effects of air resistance and friction by using a knife-edge suspension and a reversible pendulum. However, Bar Pendulum is simpler to construct and use, making it more suitable for rough measurements.
Why Kater’s pendulum is called “Kater’s Reversible Pendulum”?
Kater’s pendulum is called reversible because it can be swung from either of two pivot points, and the period of oscillation is the same from both points. This unique design allows for more accurate measurements of gravity.
What is the effective length of Kater’s Pendulum?
The effective length of Kater’s Pendulum is the distance between the centre of suspension and the centre of oscillation, which can be determined by measuring the periods of oscillation from both pivot points.
Specifically, the effective length L is given by the formula:
![\[ L = l + \frac{k^2}{l} \]](/wp-content/ql-cache/quicklatex.com-8644f134d335e9c3767d8797288e06bc_l3.png "Rendered by QuickLaTeX.com")
from
![\[ T = 2\pi\sqrt{\frac{L}{g}} \]](/wp-content/ql-cache/quicklatex.com-3f82f86c6a0e6b13a3bded31491440cf_l3.png "Rendered by QuickLaTeX.com")
where l is the distance between centre of oscillation and centre of gravity, g is the acceleration due to gravity and T is the period of oscillation.
What is the formula for calculating the value of g using Kater’s Pendulum?
![\[ g = \frac{8\pi^2 (l_1 + l_2)}{(T_1^2 + T_2^2)} \]](/wp-content/ql-cache/quicklatex.com-750dbe0a04f6968c01b5dff034cf53f2_l3.png "Rendered by QuickLaTeX.com")
You can see the full experiment here.